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Ribet}, +} +@article {Valentini-MadanZ, + AUTHOR = {Valentini, Robert C. and Madan, Manohar L.}, + TITLE = {Automorphism groups of algebraic function fields}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {176}, + YEAR = {1981}, + NUMBER = {1}, + PAGES = {39--52}, + ISSN = {0025-5874}, + CODEN = {MAZEAX}, + MRCLASS = {12A90 (14H30)}, + MRNUMBER = {MR606170 (83k:12013)}, +MRREVIEWER = {Authors' review}, + DOI = {10.1007/BF01258903}, + URL = {http://dx.doi.org/10.1007/BF01258903}, +} +@article {Schmidt:39, + AUTHOR = {Schmidt, Friedrich Karl}, + TITLE = {Zur arithmetischen {T}heorie der algebraischen {F}unktionen. + {II}. {A}llgemeine {T}heorie der {W}eierstra\ss punkte}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {45}, + YEAR = {1939}, + NUMBER = {1}, + PAGES = {75--96}, + ISSN = {0025-5874}, + CODEN = {MAZEAX}, + MRCLASS = {Contributed Item}, + MRNUMBER = {MR1545805}, + DOI = {10.1007/BF01580274}, + URL = {http://dx.doi.org/10.1007/BF01580274}, +} +@article {Cartierpoints, + AUTHOR = {Baker, Matthew H.}, + TITLE = {Cartier points on curves}, + JOURNAL = {Internat. Math. Res. Notices}, + FJOURNAL = {International Mathematics Research Notices}, + YEAR = {2000}, + NUMBER = {7}, + PAGES = {353--370}, + ISSN = {1073-7928}, + MRCLASS = {11G20 (14G05)}, + MRNUMBER = {MR1749740 (2001g:11096)}, +MRREVIEWER = {V. Kumar Murty}, + DOI = {10.1155/S1073792800000209}, + URL = {http://dx.doi.org/10.1155/S1073792800000209}, +} +@article {ValHyper, + AUTHOR = {Valentini, Robert C.}, + TITLE = {Hyperelliptic curves with zero {H}asse-{W}itt matrix}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {86}, + YEAR = {1995}, + NUMBER = {2}, + PAGES = {185--194}, + ISSN = {0025-2611}, + CODEN = {MSMHB2}, + MRCLASS = {14H45}, + MRNUMBER = {MR1317743 (96a:14035)}, +MRREVIEWER = {Luisella Caire}, + DOI = {10.1007/BF02567987}, + URL = {http://dx.doi.org/10.1007/BF02567987}, +} +@article {Laksov:84, + AUTHOR = {Laksov, Dan}, + TITLE = {Wronskians and {P}l\"ucker formulas for linear systems on + curves}, + JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. + Quatri\`eme S\'erie}, + VOLUME = {17}, + YEAR = {1984}, + NUMBER = {1}, + PAGES = {45--66}, + ISSN = {0012-9593}, + CODEN = {ASENAH}, + MRCLASS = {14H99 (14F07 14N05)}, + MRNUMBER = {MR744067 (85k:14016)}, +MRREVIEWER = {R. F. Lax}, + URL = {http://www.numdam.org/item?id=ASENS_1984_4_17_1_45_0}, +} + +@article{Adler:80, + author = {Adler, Allan}, + title = {On the automorphism groups of certain hypersurfaces}, + journal = {J. Algebra}, + year = {1981}, + volume = {72}, + number = {1}, + pages = {146--165}, + coden = {JALGA4}, + fjournal = {Journal of Algebra}, + issn = {0021-8693}, + mrclass = {14J40 (20G40)}, + mrnumber = {83g:14020}, + mrrevr = {Daniel Coray} +} +@incollection {Gille00, + AUTHOR = {Gille, Philippe}, + TITLE = {Le groupe fondamental sauvage d'une courbe affine en + caract\'eristique {$p>0$}}, + BOOKTITLE = {Courbes semi-stables et groupe fondamental en g\'eom\'etrie + alg\'ebrique ({L}uminy, 1998)}, + SERIES = {Progr. Math.}, + VOLUME = {187}, + PAGES = {217--231}, + PUBLISHER = {Birkh\"auser}, + ADDRESS = {Basel}, + YEAR = {2000}, + MRCLASS = {14H30 (14E20)}, + MRNUMBER = {MR1768103 (2002a:14027)}, +MRREVIEWER = {Antoine Chambert-Loir}, +} +@book {Langelf, + AUTHOR = {Lang, Serge}, + TITLE = {Elliptic functions}, + NOTE = {With an appendix by J. Tate}, + PUBLISHER = {Addison-Wesley Publishing Co., Inc., Reading, + Mass.-London-Amsterdam}, + YEAR = {1973}, + PAGES = {xii+326}, + MRCLASS = {10D05 (14G25 14K15 10D25)}, + MRNUMBER = {MR0409362 (53 \#13117)}, +MRREVIEWER = {Larry J. Goldstein}, +} +@book {Buch, + AUTHOR = {R.Oo Buchweitz}, + TITLE = {On Zariski's Criterion for equisingularity and non--smoothable monomial curves}, + NOTE = {Th\'ese}, + PUBLISHER = {Paris VII}, + YEAR = {1981}, + PAGES = {}, + MRCLASS = {}, + MRNUMBER = {}, +MRREVIEWER = {}, +} +@article{Lara, + author={Thomas, Lara}, + title={A valuation criterion for normal basis generators in equal + positive characteristic}, + journal={J. Algebra}, + volume={320}, + date={2008}, + number={10}, + pages={3811--3820}, + issn={0021-8693}, + review={\MR{2457723 (2009i:12007)}}, + doi={10.1016/j.jalgebra.2008.05.024}, +} +@article {IwaTa, + AUTHOR = {Iwasawa, Kenkichi and Tamagawa, Tsuneo}, + TITLE = {On the group of automorphisms of a function field}, + JOURNAL = {J. Math. Soc. Japan}, + FJOURNAL = {Journal of the Mathematical Society of Japan}, + VOLUME = {3}, + YEAR = {1951}, + PAGES = {137--147}, + ISSN = {0025-5645}, + MRCLASS = {10.0X}, + MRNUMBER = {MR0043832 (13,325b)}, +MRREVIEWER = {C. Chevalley}, +} + +@article {Sti:09, + AUTHOR = {Anbar, Nurdag{\"u}l and Stichtenoth, Henning and Tutdere, + Seher}, + TITLE = {On ramification in the compositum of function fields}, + JOURNAL = {Bull. Braz. Math. Soc. (N.S.)}, + FJOURNAL = {Bulletin of the Brazilian Mathematical Society. New Series. + Boletim da Sociedade Brasileira de Matem\'atica}, + VOLUME = {40}, + YEAR = {2009}, + NUMBER = {4}, + PAGES = {539--552}, + ISSN = {1678-7544}, + MRCLASS = {14H05 (11R58)}, + MRNUMBER = {MR2563130}, + DOI = {10.1007/s00574-009-0026-8}, + URL = {http://dx.doi.org/10.1007/s00574-009-0026-8}, +} + + +@article {Adler97, + AUTHOR = {Adler, Allan}, + TITLE = {The {M}athieu group {$M\sb {11}$} and the modular curve + {$X(11)$}}, + JOURNAL = {Proc. London Math. Soc. (3)}, + FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, + VOLUME = {74}, + YEAR = {1997}, + NUMBER = {1}, + PAGES = {1--28}, + ISSN = {0024-6115}, + CODEN = {PLMTAL}, + MRCLASS = {14G35 (11F32 11G20 14H45 20B25 20C34)}, + MRNUMBER = {MR1416724 (97k:14021)}, +MRREVIEWER = {Conjeeveram S. Rajan}, +} +@article {Boseck, + AUTHOR = {Boseck, Helmut}, + TITLE = {Zur {T}heorie der {W}eierstrasspunkte}, + JOURNAL = {Math. Nachr.}, + FJOURNAL = {Mathematische Nachrichten}, + VOLUME = {19}, + YEAR = {1958}, + PAGES = {29--63}, + ISSN = {0025-584X}, + MRCLASS = {14.00}, + MRNUMBER = {MR0106221 (21 \#4955)}, +MRREVIEWER = {H. T. Muhly}, +} +@incollection {maximalsurvey, + AUTHOR = {Garcia, Arnaldo}, + TITLE = {Curves over finite fields attaining the {H}asse-{W}eil upper + bound}, + BOOKTITLE = {European {C}ongress of {M}athematics, {V}ol. {II} + ({B}arcelona, 2000)}, + SERIES = {Progr. Math.}, + VOLUME = {202}, + PAGES = {199--205}, + PUBLISHER = {Birkh\"auser}, + ADDRESS = {Basel}, + YEAR = {2001}, + MRCLASS = {11G20 (14G15)}, + MRNUMBER = {MR1905360 (2003e:11065)}, +MRREVIEWER = {Antonio Cossidente}, +} + +@article {WpFF, + AUTHOR = {St{\"o}hr, Karl-Otto and Voloch, Jos{\'e} Felipe}, + TITLE = {Weierstrass points and curves over finite fields}, + JOURNAL = {Proc. London Math. Soc. (3)}, + FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, + VOLUME = {52}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {1--19}, + ISSN = {0024-6115}, + CODEN = {PLMTAL}, + MRCLASS = {14G15 (11G20 14G05 14G13)}, + MRNUMBER = {MR812443 (87b:14010)}, +MRREVIEWER = {R. F. Lax}, + DOI = {10.1112/plms/s3-52.1.1}, + URL = {http://dx.doi.org/10.1112/plms/s3-52.1.1}, +} + +@article {Lewittes:89, + AUTHOR = {Lewittes, Joseph}, + TITLE = {Genus and gaps in function fields}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {58}, + YEAR = {1989}, + NUMBER = {1}, + PAGES = {29--44}, + ISSN = {0022-4049}, + CODEN = {JPAAA2}, + MRCLASS = {11R58 (12F20)}, + MRNUMBER = {MR996173 (90d:11129)}, +MRREVIEWER = {James K. Deveney}, + DOI = {10.1016/0022-4049(89)90051-0}, + URL = {http://dx.doi.org/10.1016/0022-4049(89)90051-0}, +} +@article {garciaelab, + AUTHOR = {Garc{\'{\i}}a, Arnaldo}, + TITLE = {On {W}eierstrass points on certain elementary abelian + extensions of {$k(x)$}}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {17}, + YEAR = {1989}, + NUMBER = {12}, + PAGES = {3025--3032}, + ISSN = {0092-7872}, + CODEN = {COALDM}, + MRCLASS = {14H05 (11R58 14F07)}, + MRNUMBER = {MR1030607 (90m:14020)}, +MRREVIEWER = {R. F. Lax}, +} + +@article {Lewittes:90, + AUTHOR = {Lewittes, Joseph}, + TITLE = {Places of degree one in function fields over finite fields}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {69}, + YEAR = {1990}, + NUMBER = {2}, + PAGES = {177--183}, + ISSN = {0022-4049}, + CODEN = {JPAAA2}, + MRCLASS = {14C40 (11R58 14H05)}, + MRNUMBER = {MR1086559 (92b:14004)}, +MRREVIEWER = {H.-G. R{\"u}ck}, + DOI = {10.1016/0022-4049(90)90041-F}, + URL = {http://dx.doi.org/10.1016/0022-4049(90)90041-F}, +} +@article {WpPosChar, + AUTHOR = {Valentini, Robert C. and Madan, Manohar L.}, + TITLE = {Weierstrass points in characteristic {$p$}}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {247}, + YEAR = {1980}, + NUMBER = {2}, + PAGES = {123--132}, + ISSN = {0025-5831}, + CODEN = {MAANA3}, + MRCLASS = {14H05 (14F07)}, + MRNUMBER = {MR568202 (81j:14015)}, +MRREVIEWER = {R. F. Lax}, + DOI = {10.1007/BF01364138}, + URL = {http://dx.doi.org/10.1007/BF01364138}, +} + +@article {vm, + AUTHOR = {Valentini, Robert C. and Madan, Manohar L.}, + TITLE = {Automorphisms and holomorphic differentials in characteristic + {$p$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {13}, + YEAR = {1981}, + NUMBER = {1}, + PAGES = {106--115}, + ISSN = {0022-314X}, + CODEN = {JNUTA9}, + MRCLASS = {14F10}, + MRNUMBER = {MR602451 (83d:14011)}, +} + +@article {csm, + AUTHOR = {Rzedowski-Calder{\'o}n, Martha and Villa-Salvador, Gabriel and + Madan, Manohar L.}, + TITLE = {Galois module structure of holomorphic differentials in + characteristic {$p$}}, + JOURNAL = {Arch. Math. (Basel)}, + FJOURNAL = {Archiv der Mathematik}, + VOLUME = {66}, + YEAR = {1996}, + NUMBER = {2}, + PAGES = {150--156}, + ISSN = {0003-889X}, + CODEN = {ACVMAL}, + MRCLASS = {11R33 (11R58)}, + MRNUMBER = {MR1367157 (97e:11142)}, +MRREVIEWER = {Nigel Byott}, +} + + +@book{Alperin1, + author = {Alperin, J. L.}, + title = {Local representation theory}, + year = {1986}, + volume = {11}, + series = {Cambridge Studies in Advanced Mathematics}, + address = {Cambridge}, + note = {Modular representations as an introduction to the local + representation theory of finite groups}, + isbn = {0-521-30660-4; 0-521-44926-X}, + mrclass = {20-02 (20C20)}, + mrnumber = {87i:20002}, + mrreviewer = {P. Donovan}, + pages = {x+178}, + publisher = {Cambridge University Press} +} + +@incollection{Art:FormModuli, + author = {Artin, M.}, + title = {Algebraization of formal moduli. {I}}, + booktitle = {Global Analysis (Papers in Honor of K. Kodaira)}, + pages = {21--71}, + publisher = {Univ. Tokyo Press}, + year = {1969}, + address = {Tokyo}, + mrclass = {14.05}, + mrnumber = {MR0260746 (41 \#5369)}, + mrreviewer = {H. Kurke} +} + +@article {Atkin-Lehner, + + AUTHOR = {Atkin, A. O. L. and Lehner, J.}, + + TITLE = {Hecke operators on {$\Gamma \sb{0}(m)$}}, + + JOURNAL = {Math. Ann.}, + + FJOURNAL = {Mathematische Annalen}, + + VOLUME = {185}, + + YEAR = {1970}, + + PAGES = {134--160}, + + ISSN = {0025-5831}, + + MRCLASS = {10.20}, + + MRNUMBER = {MR0268123 (42 \#3022)}, + +MRREVIEWER = {R. A. Rankin}, + +} + + + +@incollection {BeCaGu, + + AUTHOR = {Bending, Peter and Camina, Alan and Guralnick, Robert}, + + TITLE = {Automorphisms of the modular curve}, + + BOOKTITLE = {Progress in Galois theory}, + + SERIES = {Dev. Math.}, + + VOLUME = {12}, + + PAGES = {25--37}, + + PUBLISHER = {Springer}, + + ADDRESS = {New York}, + + YEAR = {2005}, + + MRCLASS = {14H37 (14G35)}, + + MRNUMBER = {MR2148458 (2006c:14050)}, + +MRREVIEWER = {Rolf Berndt}, + +} + + + +@article{Be-Me, + author = {Bertin, Jos{\'e} and M{\'e}zard, Ariane}, + title = {D\'eformations formelles des rev\^etements sauvagement ramifi\'es de courbes alg\'ebriques}, + journal = {Invent. Math.}, + year = 2000, + volume = {141}, + number = 1, + pages = {195--238}, + file = {/home/kontogar/Papers/pdf/bertinMeazInv.pdf}, + coden = {INVMBH}, + fjournal = {Inventiones Mathematicae}, + issn = {0020-9910}, + mrclass = {14D15 (14D20 14H10 14H30 14H37)}, + mrnumber = {2001f:14023}, + mrreviewer = {Akio Tamagawa} +} +@article {Val:82, + AUTHOR = {Valentini, Robert C.}, + TITLE = {Representations of automorphisms on differentials of function + fields of characteristic {$p$}}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {335}, + YEAR = {1982}, + PAGES = {164--179}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {12A90 (14H05)}, + MRNUMBER = {MR667465 (84j:12013)}, +MRREVIEWER = {Author's review}, + DOI = {10.1515/crll.1982.335.164}, + URL = {http://dx.doi.org/10.1515/crll.1982.335.164}, +} + +@book {HungerBo, + AUTHOR = {Hungerford, Thomas W.}, + TITLE = {Algebra}, + PUBLISHER = {Holt}, + ADDRESS = {Rinehart and Winston, Inc., New York}, + YEAR = {1974}, + PAGES = {xix+502}, + MRCLASS = {00A05}, + MRNUMBER = {MR0354211 (50 \#6693)}, +MRREVIEWER = {F. De Meyer}, +} + + +@article {Salvador:00, + AUTHOR = {L{\'o}pez-Bautista, Pedro Ricardo and Villa-Salvador, Gabriel + Daniel}, + TITLE = {On the {G}alois module structure of semisimple holomorphic + differentials}, + JOURNAL = {Israel J. Math.}, + FJOURNAL = {Israel Journal of Mathematics}, + VOLUME = {116}, + YEAR = {2000}, + PAGES = {345--365}, + ISSN = {0021-2172}, + CODEN = {ISJMAP}, + MRCLASS = {12F10 (14H05)}, + MRNUMBER = {MR1759412 (2001f:12007)}, +MRREVIEWER = {Ivan D. Chipchakov}, + DOI = {10.1007/BF02773225}, + URL = {http://dx.doi.org/10.1007/BF02773225}, +} + + + +@article {Madden78, + AUTHOR = {Madden, Daniel J.}, + TITLE = {Arithmetic in generalized {A}rtin-{S}chreier extensions of + {$k(x)$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {10}, + YEAR = {1978}, + NUMBER = {3}, + PAGES = {303--323}, + ISSN = {0022-314X}, + CODEN = {JNUTA9}, + MRCLASS = {12A90 (14H05)}, + MRNUMBER = {MR506641 (80d:12009)}, +MRREVIEWER = {M. Fried}, + DOI = {10.1016/0022-314X(78)90027-6}, + URL = {http://dx.doi.org/10.1016/0022-314X(78)90027-6}, +} + +@article {Tamagawa:51, + AUTHOR = {Tamagawa, Tuneo}, + TITLE = {On unramified extensions of algebraic function fields}, + JOURNAL = {Proc. Japan Acad.}, + FJOURNAL = {Proceedings of the Japan Academy}, + VOLUME = {27}, + YEAR = {1951}, + PAGES = {548--551}, + ISSN = {0021-4280}, + MRCLASS = {10.0X}, + MRNUMBER = {MR0047705 (13,918a)}, +MRREVIEWER = {O. F. G. Schilling}, +} + + +@article{BertinCRAS, + author = {Bertin, Jos{\'e}}, + title = {Obstructions locales au rel\`evement de rev\^etements galoisiens de courbes lisses}, + journal = {C. R. Acad. Sci. Paris S\'er. I Math.}, + year = 1998, + volume = {326}, + number = 1, + pages = {55--58}, + file = {/media/KINGSTON-1/Papers/pdf/beertincrash.pdf}, + coden = {CASMEI}, + fjournal = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, + issn = {0764-4442}, + mrclass = {14H30}, + mrnumber = {99h:14032} +} + +@article {Teitelbaum90, + AUTHOR = {Teitelbaum, Jeremy T.}, + TITLE = {Values of {$p$}-adic {$L$}-functions and a {$p$}-adic + {P}oisson kernel}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {101}, + YEAR = {1990}, + NUMBER = {2}, + PAGES = {395--410}, + ISSN = {0020-9910}, + CODEN = {INVMBH}, + MRCLASS = {11F33 (11F67 11F85)}, + MRNUMBER = {1062968 (91m:11034)}, +MRREVIEWER = {Ehud de Shalit}, + DOI = {10.1007/BF01231508}, + URL = {http://dx.doi.org/10.1007/BF01231508}, +} + +@incollection {Schneider84, + AUTHOR = {Schneider, P.}, + TITLE = {Rigid-analytic {$L$}-transforms}, + BOOKTITLE = {Number theory, {N}oordwijkerhout 1983 ({N}oordwijkerhout, + 1983)}, + SERIES = {Lecture Notes in Math.}, + VOLUME = {1068}, + PAGES = {216--230}, + PUBLISHER = {Springer}, + ADDRESS = {Berlin}, + YEAR = {1984}, + MRCLASS = {11F85 (11G40 14G10)}, + MRNUMBER = {756097 (86b:11043)}, +MRREVIEWER = {K. Shiratani}, + DOI = {10.1007/BFb0099455}, + URL = {http://dx.doi.org/10.1007/BFb0099455}, +} + + +@article {KoYang, + AUTHOR = {Kontogeorgis, Aristides and Yang, Yifan}, + TITLE = {Automorphisms of hyperelliptic modular curves {$X_0(N)$} in + positive characteristic}, + JOURNAL = {LMS J. Comput. Math.}, + FJOURNAL = {LMS Journal of Computation and Mathematics}, + VOLUME = {13}, + YEAR = {2010}, + PAGES = {144--163}, + ISSN = {1461-1570}, + MRCLASS = {14G35 (11F11 11G20 14H37)}, + MRNUMBER = {2638986}, +} + +@article{Belyi1, + author = {Bely{\u\i}, G. V.}, + title = {Galois extensions of a maximal cyclotomic field}, + journal = {Izv. Akad. Nauk SSSR Ser. Mat.}, + year = {1979}, + volume = {43}, + number = {2}, + pages = {267--276, 479}, + fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, + issn = {0373-2436}, + mrclass = {12A55}, + mrnumber = {MR534593 (80f:12008)}, + mrreviewer = {J. Browkin} +} + +@article{BeMe2002Man, + author = {Bertin, Jos{\'e} and M{\'e}zard, Ariane}, + title = {Problem of formation of quotients and base change}, + journal = {Manuscripta Math.}, + year = 2004, + volume = {115}, + number = 4, + pages = {467--487}, + coden = {MSMHB2}, + fjournal = {Manuscripta Mathematica}, + issn = {0025-2611}, + mrclass = {14L30}, + mrnumber = {MR2103662 (2006b:14081)}, + mrreviewer = {Amnon Neeman} +} + +@article {BraStich86, + AUTHOR = {Brandt, Rolf and Stichtenoth, Henning}, + TITLE = {Die {A}utomorphismengruppen hyperelliptischer {K}urven}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {55}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {83--92}, + ISSN = {0025-2611}, + CODEN = {MSMHB2}, + MRCLASS = {14H45 (20B25)}, + MRNUMBER = {MR828412 (87m:14033)}, +MRREVIEWER = {Shoichi Nakajima}, +} + + +@article{BradleyCyc, + author = {Patrick Erik Bradley}, + title = {{Cyclic {Coverings} of the $p$-adic projective line by {M}umford {C}urves}}, + journal = {preprint}, + +} + +@article{CKK, + author = {Cornelissen, Gunther and Kato, Fumiharu and Kontogeorgis, Aristides}, + title = {Discontinuous groups in positive characteristic and automorphisms of {M}umford curves}, + journal = {Math. Ann.}, + year = 2001, + volume = {320}, + number = 1, + pages = {55--85}, + file = {/media/KINGSTON/Papers/pdf/D3.pdf}, + coden = {MAANA}, + fjournal = {Mathematische Annalen}, + issn = {0025-5831}, + mrclass = {14Gxx (11Gxx)}, + mrnumber = {1 835 062} +} + +@article{CK, + author = {Cornelissen, Gunther and Kato, Fumiharu}, + title = {Equivariant deformation of {M}umford curves and of ordinary + curves in positive characteristic}, + journal = {Duke Math. J.}, + year = {2003}, + volume = {116}, + number = {3}, + pages = {431--470}, + coden = {DUMJAO}, + fjournal = {Duke Mathematical Journal}, + issn = {0012-7094}, + mrclass = {14G22 (14D15 14H37)}, + mrnumber = {MR1958094 (2004c:14044)}, + mrreviewer = {Letterio Gatto} +} + +@article{CKNotices, + author = {Cornelissen, Gunther and Kato, Fumiharu}, + title = {The {$p$}-adic icosahedron}, + journal = {Notices Amer. Math. Soc.}, + year = {2005}, + volume = {52}, + number = {7}, + pages = {720--727}, + coden = {AMNOAN}, + fjournal = {Notices of the American Mathematical Society}, + issn = {0002-9920}, + mrclass = {52B12 (14H25)}, + mrnumber = {MR2159689} +} + +@article{DelMum, + author = {Deligne, P. and Mumford, D.}, + title = {The irreducibility of the space of curves of given genus}, + journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, + year = {1969}, + number = {36}, + pages = {75--109}, + mrclass = {14.20}, + mrnumber = {41 \#6850}, + mrreviewer = {Manfred Herrmann} +} + +@book{Eisenbud:95, + author = {Eisenbud, David}, + title = {Commutative algebra}, + year = {1995}, + address = {New York}, + note = {With a view toward algebraic geometry}, + isbn = {0-387-94268-8; 0-387-94269-6}, + pages = {xvi+785}, + publisher = {Springer-Verlag} +} + +@book{GeKaZe:94, + author = {Gelfand, I. M. and Kapranov, M. M. and Zelevinsky, A. + V.}, + title = {Discriminants, resultants, and multidimensional determinants}, + year = {1994}, + address = {Boston, MA}, + isbn = {0-8176-3660-9}, + pages = {x+523}, + publisher = {Birkh\"auser Boston Inc.} +} + +@article{Geer-Vlugt92, + author = {van der Geer, Gerard and van der Vlugt, Marcel}, + title = {Reed-{M}uller codes and supersingular curves. {I}}, + journal = {Compositio Math.}, + year = {1992}, + volume = {84}, + number = {3}, + pages = {333--367}, + coden = {CMPMAF}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {14H25 (11G20 94B27)}, + mrnumber = {MR1189892 (93k:14038)}, + mrreviewer = {R. F. Lax} +} + +@book{Ge-Pu, + author = {Gerritzen, Lothar and van der Put, Marius}, + title = {Schottky groups and {M}umford curves}, + year = {1980}, + volume = {817}, + series = {Lecture Notes in Mathematics}, + address = {Berlin}, + isbn = {3-540-10229-9}, + mrclass = {10D30 (14H25 32J99 32K15)}, + mrnumber = {MR590243 (82j:10053)}, + mrreviewer = {V. V. Shokurov}, + pages = {viii+317}, + publisher = {Springer} +} + +@book{Gou:97, + author = {Gouv\^{e}a, Fernando Q.}, + title = {$p$-adic numbers}, + year = {1997}, + address = {Berlin}, + edition = {Second}, + note = {An introduction}, + isbn = {3-540-62911-4}, + mrclass = {11S80 (11-01 12J25)}, + mrnumber = {98h:11155}, + pages = {vi+298}, + publisher = {Springer-Verlag} +} + +@book{Griffiths-Harris:95, + author = {Griffiths, Phillip and Harris, Joseph}, + title = {Principles of algebraic geometry}, + year = {1994}, + address = {New York}, + note = {Reprint of the 1978 original}, + isbn = {0-471-05059-8}, + pages = {xiv+813}, + publisher = {John Wiley \& Sons Inc.} +} + +@article{GroTo, + author = {Grothendieck, Alexander}, + title = {Sur quelques points d'alg\`ebre homologique}, + journal = {T\^ohoku Math. J. (2)}, + year = {1957}, + volume = {9}, + pages = {119--221}, + mrclass = {18.00}, + mrnumber = {21 \#1328}, + mrreviewer = {D. Buchsbaum} +} +@book {GroFGA, + AUTHOR = {Grothendieck, Alexander}, + TITLE = {Fondements de la g\'eom\'etrie alg\'ebrique. [{E}xtraits du + {S}\'eminaire {B}ourbaki, 1957--1962.]}, + PUBLISHER = {Secr\'etariat math\'ematique}, + ADDRESS = {Paris}, + YEAR = {1962}, + PAGES = {ii+205}, + MRCLASS = {14.00}, + MRNUMBER = {MR0146040 (26 \#3566)}, +MRREVIEWER = {E. L. Griffin, Jr.}, +} + +@book {HaleKocak, + AUTHOR = {Hale, Jack K. and Ko{\c{c}}ak, H{\"u}seyin}, + TITLE = {Dynamics and bifurcations}, + SERIES = {Texts in Applied Mathematics}, + VOLUME = {3}, + PUBLISHER = {Springer-Verlag}, + ADDRESS = {New York}, + YEAR = {1991}, + PAGES = {xiv+568}, + ISBN = {0-387-97141-6}, + MRCLASS = {58Fxx (34-01 34C23 58-01 58F14)}, + MRNUMBER = {MR1138981 (93e:58047)}, +MRREVIEWER = {D. R. J. Chillingworth}, +} + +@incollection {HarMSRI03, + AUTHOR = {Harbater, David}, + TITLE = {Patching and {G}alois theory}, + BOOKTITLE = {Galois groups and fundamental groups}, + SERIES = {Math. Sci. Res. Inst. Publ.}, + VOLUME = {41}, + PAGES = {313--424}, + PUBLISHER = {Cambridge Univ. Press}, + ADDRESS = {Cambridge}, + YEAR = {2003}, + MRCLASS = {14H30 (12F12 14G22)}, + MRNUMBER = {MR2012220 (2004j:14030)}, +MRREVIEWER = {Robert M. Guralnick}, +} + +@article {HarStevJA99, + AUTHOR = {Harbater, David and Stevenson, Katherine F.}, + TITLE = {Patching and thickening problems}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {212}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {272--304}, + ISSN = {0021-8693}, + CODEN = {JALGA4}, + MRCLASS = {14B10 (12F12 14B12 14H30)}, + MRNUMBER = {MR1670658 (2000b:14004)}, +MRREVIEWER = {Hiroaki Nakamura}, +} + + + +@book{HarrisModuli, + author = {Harris, Joe and Morrison, Ian}, + title = {Moduli of curves}, + year = {1998}, + volume = {187}, + series = {Graduate Texts in Mathematics}, + address = {New York}, + isbn = {0-387-98438-0; 0-387-98429-1}, + mrclass = {14H10 (14-02 14D20 14D22)}, + mrnumber = {MR1631825 (99g:14031)}, + mrreviewer = {R. F. Lax}, + pages = {xiv+366}, + publisher = {Springer-Verlag} +} + +@book{HarDef, + author = {Hartshorne, Robin}, + title = {Lectures on Deformation Theory}, + year = {2004}, + address = {}, + note = {}, + isbn = {}, + pages = {163}, + publisher = {available online on authors webpage} +} + +@book{Hartshorne:77, + author = {Hartshorne, Robin}, + title = {Algebraic {G}eometry}, + year = {1977}, + address = {New York}, + note = {Graduate Texts in Mathematics, No. 52}, + isbn = {0-387-90244-9}, + pages = {xvi+496}, + publisher = {Springer-Verlag} +} + +@article{Hart:Coherent, + author = {Hartshorne, Robin}, + title = {Coherent functors}, + journal = {Adv. Math.}, + year = {1998}, + volume = {140}, + number = {1}, + pages = {44--94}, + coden = {ADMTA4}, + fjournal = {Advances in Mathematics}, + issn = {0001-8708}, + mrclass = {14F05 (14A99 14M06)}, + mrnumber = {MR1656482 (2000a:14018)}, + mrreviewer = {Liam O'Carroll} +} + +@incollection {wildthings, + AUTHOR = {du Sautoy, Marcus and Fesenko, Ivan}, + TITLE = {Where the wild things are: ramification groups and the + {N}ottingham group}, + BOOKTITLE = {New horizons in pro-{$p$} groups}, + SERIES = {Progr. Math.}, + VOLUME = {184}, + PAGES = {287--328}, + PUBLISHER = {Birkh\"auser Boston}, + ADDRESS = {Boston, MA}, + YEAR = {2000}, + MRCLASS = {20E18 (11S15)}, + MRNUMBER = {MR1765125 (2001h:20034)}, +MRREVIEWER = {Martyn Quick}, +} + + + + + +@article{Henn:78, + author = {Henn, Hans-Wolfgang}, + title = {Funktionenk\"orper mit grosser {A}utomorphismengruppe}, + journal = {J. Reine Angew. Math.}, + year = {1978}, + volume = {302}, + pages = {96--115}, + coden = {JRMAA8}, + fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, + issn = {0075-4102}, + mrclass = {14H05 (12A90)}, + mrnumber = {80a:14012}, + mrreviewer = {R. F. Lax} +} + +@book {Curtis-Reiner, + AUTHOR = {Curtis, Charles W. and Reiner, Irving}, + TITLE = {Representation theory of finite groups and associative + algebras}, + NOTE = {Reprint of the 1962 original}, + PUBLISHER = {AMS Chelsea Publishing, Providence, RI}, + YEAR = {2006}, + PAGES = {xiv+689}, + ISBN = {0-8218-4066-5}, + MRCLASS = {16-02 (20-02 20Cxx)}, + MRNUMBER = {2215618 (2006m:16001)}, +} + + +@article{Herrlich:80, + author = {Herrlich, Frank}, + title = {Die {O}rdnung der {A}utomorphismengruppe einer {$p$}-adischen + {S}chottkykurve}, + journal = {Math. Ann.}, + year = {1979/80}, + volume = {246}, + number = {2}, + pages = {125--130}, + coden = {MAANA3}, + fjournal = {Mathematische Annalen}, + issn = {0025-5831}, + mrclass = {14H30 (14G20)}, + mrnumber = {MR564682 (81f:14015)}, + mrreviewer = {M. Kh. Gizatullin} +} + +@article{Hu:1893, + author = {Adolf Hurwitz}, + title = {{\"U}ber algebraische {G}ebilde mit eindeutigen {T}ranformationen + in sich}, + journal = {Math. Ann.}, + year = {1893}, + volume = {41}, + pages = {403--442}, + +} + +@book{Hu:67, + author = {Huppert, B.}, + title = {Endliche {G}ruppen. {I}}, + year = {1967}, + address = {Berlin}, + note = {Die Grundlehren der Mathematischen Wissenschaften, Band 134}, + pages = {xii+793}, + publisher = {Springer-Verlag} +} + +@article{Hoch-Serre, + author = {Hochschild, G. and Serre, J.-P.}, + title = {Cohomology of group extensions}, + journal = {Trans. Amer. Math. Soc.}, + year = {1953}, + volume = {74}, + pages = {110--134}, + mrclass = {20.0X}, + mrnumber = {14,619b}, + mrreviewer = {H. Cartan} +} + + + + +@book{Jac2, + author = {Jacobson, Nathan}, + title = {Basic algebra. {I}{I}}, + year = {1989}, + address = {New York}, + edition = {Second}, + isbn = {0-7167-1933-9}, + mrclass = {00A05 (12-01 15-01 16-01)}, + mrnumber = {90m:00007}, + mrreviewer = {P. M. Cohn}, + pages = {xviii+686}, + publisher = {W. H. Freeman and Company} +} + +@book {MR780184, + AUTHOR = {Jacobson, Nathan}, + TITLE = {Basic algebra. {I}}, + EDITION = {Second}, + PUBLISHER = {W. H. Freeman and Company, New York}, + YEAR = {1985}, + PAGES = {xviii+499}, + ISBN = {0-7167-1480-9}, + MRCLASS = {00A05 (12-01)}, + MRNUMBER = {780184}, +} + +@article {Igusa59, + + AUTHOR = {Igusa, Jun-ichi}, + + TITLE = {Kroneckerian model of fields of elliptic modular functions}, + + JOURNAL = {Amer. J. Math.}, + + FJOURNAL = {American Journal of Mathematics}, + + VOLUME = {81}, + + YEAR = {1959}, + + PAGES = {561--577}, + + ISSN = {0002-9327}, + + MRCLASS = {14.00 (10.00)}, + + MRNUMBER = {MR0108498 (21 \#7214)}, + +MRREVIEWER = {M. Rosenlicht}, + +} + + + +@mastersthesis{Kai-wen-lan, + author = {Kai Wen Lan}, + title = {Moduli Schemes of Elliptic Curves}, + school = {National Taiwan University}, + year = {2001}, + +} + +@article{OrbifoldKato, + author = {Kato, Fumiharu}, + title = {Non-{A}rchimedean orbifolds covered by {M}umford curves}, + journal = {J. Algebraic Geom.}, + year = 2005, + volume = {14}, + number = 1, + pages = {1--34}, + file = {/home/kontogar/Papers/pdf/katoJAG.pdf}, + fjournal = {Journal of Algebraic Geometry}, + issn = {1056-3911}, + mrclass = {14G22 (20G25)}, + mrnumber = {MR2092125 (2005h:14058)}, + mrreviewer = {Marco A. Garuti} +} + +@article{KatoTriangle, + author = {Kato, Fumiharu}, + title = {$p$-adic {S}chwarzian triangle groups of {M}umford type}, + journal = {preprint}, + +} + +@article{Kallel-Sjerve, + author = {Kallel, Sadok and Sjerve, Denis}, + title = {On the group of automorphisms of cyclic covers of the + {R}iemann sphere}, + journal = {Math. Proc. Cambridge Philos. Soc.}, + year = {2005}, + volume = {138}, + number = {2}, + pages = {267--287}, + coden = {MPCPCO}, + fjournal = {Mathematical Proceedings of the Cambridge Philosophical + Society}, + issn = {0305-0041}, + mrclass = {20H10 (20H15 30F35)}, + mrnumber = {MR2132169} +} + +@article {SK, + AUTHOR = {Karanikolopoulos, Sotiris and Kontogeorgis, Aristides}, + TITLE = {Representation of cyclic groups in positive characteristic and + {W}eierstrass semigroups}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {133}, + YEAR = {2013}, + NUMBER = {1}, + PAGES = {158--175}, + ISSN = {0022-314X}, + CODEN = {JNUTA9}, + MRCLASS = {Preliminary Data}, + MRNUMBER = {2981406}, + DOI = {10.1016/j.jnt.2012.05.039}, + URL = {http://dx.doi.org/10.1016/j.jnt.2012.05.039}, +} + + AUTHOR = {Karanikolopoulos, Sotiris and Kontogeorgis Aristides}, + TITLE = {Representations of cyclic groups in positive characteristic and Weierstrass semigroups}, + JOURNAL = {arXiv:1107.4849}, + YEAR = {2011}, + +} + +@article {karan, + AUTHOR = {Karanikolopoulos, Sotiris}, + TITLE = {On holomorphic polydifferentials in positive characteristic}, + JOURNAL = {Math. Nachr.}, + FJOURNAL = {Mathematische Nachrichten}, + VOLUME = {285}, + YEAR = {2012}, + NUMBER = {7}, + PAGES = {852--877}, + ISSN = {0025-584X}, + MRCLASS = {14Fxx (11G20)}, + MRNUMBER = {2924517}, + DOI = {10.1002/mana.201000114}, + URL = {http://dx.doi.org/10.1002/mana.201000114}, +} + + +@article {Ant, + AUTHOR = {Antoniadis, Jannis}, + TITLE = {Representation Theory Of Finite Groups, available at http://myria.math.aegean.gr/~kontogar/Reps2009/index.html}, + JOURNAL = {(in greek)}, + YEAR = {1998}, + URL = {available at http://myria.math.aegean.gr/~kontogar/Reps2009/index.html} +} +@article {KatoDuke87, + AUTHOR = {Kato, Kazuya}, + TITLE = {Vanishing cycles, ramification of valuations, and class field + theory}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {55}, + YEAR = {1987}, + NUMBER = {3}, + PAGES = {629--659}, + ISSN = {0012-7094}, + CODEN = {DUMJAO}, + MRCLASS = {11S15 (11S31 11S70 19F27)}, + MRNUMBER = {MR904945 (88k:11083)}, +MRREVIEWER = {J. Browkin}, +} + + +@book{KaMa, + author = {Katz, Nicholas M. and Mazur, Barry}, + title = {Arithmetic moduli of elliptic curves}, + year = 1985, + address = {Princeton, NJ}, + file = {/home/kontogar/Papers/pdf/Katz, Mazur - Arithmetic Moduli of Elliptic Curves (PUP 1985).pdf}, + isbn = {0-691-08349-5; 0-691-08352-5}, + mrclass = {11G05 (11F11 14G25 14K15)}, + mrnumber = {86i:11024}, + mrreviewer = {Kenneth A. Ribet}, + pages = {xiv+514}, + publisher = {Princeton University Press} +} + +@article{KPS, + author = {Karrass, A. and Pietrowski, A. and Solitar, D.}, + title = {Finite and infinite cyclic extensions of free groups}, + journal = {J. Austral. Math. Soc.}, + year = {1973}, + volume = {16}, + pages = {458--466}, + note = {Collection of articles dedicated to the memory of Hanna + Neumann, IV}, + fjournal = {Australian Mathematical Society. Journal. Series A. Pure + Mathematics and Statistics}, + issn = {0263-6115}, + mrclass = {20F05}, + mrnumber = {MR0349850 (50 \#2343)}, + mrreviewer = {Stephen Meskin} +} + +@inproceedings{Kl:86, + author = {Kleiman, Steven L.}, + title = {Tangency and duality}, + booktitle = {Proceedings of the 1984 Vancouver conference in algebraic + geometry}, + pages = {163--225}, + year = {1986}, + address = {Providence, R.I.}, + publisher = {Amer. Math. Soc.}, + +} + +@incollection{Kl-Pi:91, + author = {Kleiman, Steven and Piene, Ragni}, + title = {On the inseparability of the {G}auss map}, + booktitle = {Enumerative algebraic geometry (Copenhagen, 1989)}, + pages = {107--129}, + publisher = {Amer. Math. Soc.}, + year = {1991}, + address = {Providence, RI}, + +} + +@article {homma92, + AUTHOR = {Homma, Masaaki}, + TITLE = {Linear systems on curves with no {W}eierstrass points}, + JOURNAL = {Bol. Soc. Brasil. Mat. (N.S.)}, + FJOURNAL = {Boletim da Sociedade Brasileira de Matem\'atica. Nova S\'erie}, + VOLUME = {23}, + YEAR = {1992}, + NUMBER = {1-2}, + PAGES = {93--108}, + ISSN = {0100-3569}, + MRCLASS = {14H55}, + MRNUMBER = {MR1203175 (94c:14028)}, +MRREVIEWER = {Angelo Lopez}, +} + + +@article {pardini, + AUTHOR = {Pardini, Rita}, + TITLE = {Some remarks on plane curves over fields of finite + characteristic}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {60}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {3--17}, + ISSN = {0010-437X}, + CODEN = {CMPMAF}, + MRCLASS = {14N10 (14E05 14H45)}, + MRNUMBER = {MR867952 (88c:14069)}, +MRREVIEWER = {Ragni Piene}, + URL = {http://www.numdam.org/item?id=CM_1986__60_1_3_0}, +} + +@article {hefez89, + AUTHOR = {Hefez, Abramo}, + TITLE = {Nonreflexive curves}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {69}, + YEAR = {1989}, + NUMBER = {1}, + PAGES = {3--35}, + ISSN = {0010-437X}, + CODEN = {CMPMAF}, + MRCLASS = {14H45}, + MRNUMBER = {MR986811 (90k:14028)}, + URL = {http://www.numdam.org/item?id=CM_1989__69_1_3_0}, +} + + +@article {gv, + AUTHOR = {Garc{\'{\i}}a, Arnaldo and Voloch, J. F.}, + TITLE = {Wronskians and linear independence in fields of prime + characteristic}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {59}, + YEAR = {1987}, + NUMBER = {4}, + PAGES = {457--469}, + ISSN = {0025-2611}, + CODEN = {MSMHB2}, + MRCLASS = {12F15 (14H05)}, + MRNUMBER = {MR915997 (88m:12005)}, +MRREVIEWER = {B. Heinrich Matzat}, + DOI = {10.1007/BF01170848}, + URL = {http://dx.doi.org/10.1007/BF01170848}, +} + + + +@article{Ko:98, + author = {Kontogeorgis, Aristides I.}, + title = {The group of automorphisms of the function fields of the curve $x\sp n+y\sp m+1=0$}, + journal = {J. Number Theory}, + year = 1998, + volume = {72}, + number = 1, + pages = {110--136}, + file = {/home/kontogar/Papers/pdf/D1.pdf}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X} +} +@article{KontoZ, + AUTHOR = {Kontogeorgis, A.}, + TITLE = {The ramification sequence for a fixed point of an automorphism + of a curve and the {W}eierstrass gap sequence}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {259}, + YEAR = {2008}, + NUMBER = {3}, + PAGES = {471--479}, + ISSN = {0025-5874}, + CODEN = {MAZEAX}, + MRCLASS = {14H55 (14H37)}, + MRNUMBER = {MR2395122 (2009a:14041)}, +MRREVIEWER = {Eleonora Palmieri}, + DOI = {10.1007/s00209-007-0231-3}, + URL = {http://dx.doi.org/10.1007/s00209-007-0231-3}, +} + + +@article {Hasse-Witt, + AUTHOR = {Hasse, Helmut and Witt, Ernst}, + TITLE = {Zyklische unverzweigte {E}rweiterungsk\"orper vom + {P}rimzahlgrade {$p$} \"uber einem algebraischen + {F}unktionenk\"orper der {C}harakteristik {$p$}}, + JOURNAL = {Monatsh. Math. Phys.}, + FJOURNAL = {Monatshefte f\"ur Mathematik und Physik}, + VOLUME = {43}, + YEAR = {1936}, + NUMBER = {1}, + PAGES = {477--492}, + ISSN = {0026-9255}, + MRCLASS = {Contributed Item}, + MRNUMBER = {MR1550551}, + DOI = {10.1007/BF01707628}, + URL = {http://dx.doi.org/10.1007/BF01707628}, +} + +@article {Stoehr-Vianna, + AUTHOR = {St{\"o}hr, Karl-Otto and Viana, Paulo}, + TITLE = {A study of {H}asse-{W}itt matrices by local methods}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {200}, + YEAR = {1989}, + NUMBER = {3}, + PAGES = {397--407}, + ISSN = {0025-5874}, + CODEN = {MAZEAX}, + MRCLASS = {11G20 (14G15 14H30)}, + MRNUMBER = {MR978599 (90d:11074)}, +MRREVIEWER = {Ren{\'e} Schoof}, + DOI = {10.1007/BF01215655}, + URL = {http://dx.doi.org/10.1007/BF01215655}, +} +@article {Ro, + AUTHOR = {Rocher, Magali}, + TITLE = {Large {$p$}-group actions with a {$p$}-elementary abelian + derived group}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {321}, + YEAR = {2009}, + NUMBER = {2}, + PAGES = {704--740}, + ISSN = {0021-8693}, + CODEN = {JALGA4}, + MRCLASS = {14H37}, + MRNUMBER = {MR2483289 (2010a:14059)}, +MRREVIEWER = {Jennifer Paulhus}, + DOI = {10.1016/j.jalgebra.2008.09.030}, + URL = {http://dx.doi.org/10.1016/j.jalgebra.2008.09.030}, +} + +@article {Ma-Ro, + AUTHOR = {Matignon, Michel and Rocher, Magali}, + TITLE = {Smooth curves having a large automorphism {$p$}-group in + characteristic {$p>0$}}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {2}, + YEAR = {2008}, + NUMBER = {8}, + PAGES = {887--926}, + ISSN = {1937-0652}, + MRCLASS = {14H37 (11R37)}, + MRNUMBER = {MR2457356}, +} +@article {RiReJA, + AUTHOR = {Re, Riccardo}, + TITLE = {The rank of the {C}artier operator and linear systems on + curves}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {236}, + YEAR = {2001}, + NUMBER = {1}, + PAGES = {80--92}, + ISSN = {0021-8693}, + CODEN = {JALGA4}, + MRCLASS = {14C20 (14F10 14H99)}, + MRNUMBER = {MR1808346 (2002c:14016)}, +MRREVIEWER = {C{\'{\i}}cero Fernandes de Carvalho}, + DOI = {10.1006/jabr.2000.8479}, + URL = {http://dx.doi.org/10.1006/jabr.2000.8479}, +} + +@article {Komiya, + AUTHOR = {Komiya, Kaname}, + TITLE = {Algebraic curves with non-classical types of gap sequences for + genus three and four}, + JOURNAL = {Hiroshima Math. J.}, + FJOURNAL = {Hiroshima Mathematical Journal}, + VOLUME = {8}, + YEAR = {1978}, + NUMBER = {2}, + PAGES = {371--400}, + ISSN = {0018-2079}, + MRCLASS = {14H20}, + MRNUMBER = {MR0498586 (58 \#16680)}, +MRREVIEWER = {Jayant M. Shah}, +} + +@article {Oliv2, + AUTHOR = {Oliveira, Gilvan and St{\"o}hr, Karl-Otto}, + TITLE = {Gorenstein curves with quasi-symmetric {W}eierstrass + semigroups}, + JOURNAL = {Geom. Dedicata}, + FJOURNAL = {Geometriae Dedicata}, + VOLUME = {67}, + YEAR = {1997}, + NUMBER = {1}, + PAGES = {45--63}, + ISSN = {0046-5755}, + CODEN = {GEMDAT}, + MRCLASS = {14H55 (14H10)}, + MRNUMBER = {MR1468860 (98h:14035a)}, +MRREVIEWER = {R. F. Lax}, + DOI = {10.1023/A:1004995513658}, + URL = {http://dx.doi.org/10.1023/A:1004995513658}, +} + + + +@article {Oliv, + AUTHOR = {Oliveira, Gilvan}, + TITLE = {Weierstrass semigroups and the canonical ideal of nontrigonal + curves}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {71}, + YEAR = {1991}, + NUMBER = {4}, + PAGES = {431--450}, + ISSN = {0025-2611}, + CODEN = {MSMHB2}, + MRCLASS = {14H55}, + MRNUMBER = {MR1104994 (92c:14028)}, +MRREVIEWER = {Jean D'Almeida}, + DOI = {10.1007/BF02568416}, + URL = {http://dx.doi.org/10.1007/BF02568416}, +} +@book{RitzNotes, + author = {Ritzenthaler, Christophe}, + title = {Curves Over Finite Fields, courses notes, available at www.math.jussieu.fr/ritzenth.}, + year = {2005}, + comment={available at www.math.jussieu.fr/-ritzenth.}, + address = {}, + isbn = {}, + mrclass = {}, + mrnumber = {}, + mrreviewer = {}, + pages = {}, + publisher = {Barcelona University UPC} +} + +@article{Torres00, + author = {Torres, Fernando}, + title = {The approach of {S}t\"ohr-{V}oloch to the {H}asse-{W}eil bound with applications to optimal curves and plane arcs}, + journal = {arXiv:math/0011091v1}, + year = {2000}, + volume = {}, + number = {}, + pages = {}, + coden = {}, + fjournal = {}, + issn = {}, + mrclass = {}, + mrnumber = {}, + mrreviewer = {} +} +@article {GarciaTafazolian, + AUTHOR = {Garcia, Arnaldo and Tafazolian, Saeed}, + TITLE = {Certain maximal curves and {C}artier operators}, + JOURNAL = {Acta Arith.}, + FJOURNAL = {Acta Arithmetica}, + VOLUME = {135}, + YEAR = {2008}, + NUMBER = {3}, + PAGES = {199--218}, + ISSN = {0065-1036}, + CODEN = {AARIA9}, + MRCLASS = {11G20 (11M38)}, + MRNUMBER = {MR2457195 (2009i:11076)}, +MRREVIEWER = {S. A. Stepanov}, + DOI = {10.4064/aa135-3-1}, + URL = {http://dx.doi.org/10.4064/aa135-3-1}, +} + +@article{KontoANT, + AUTHOR = {Kontogeorgis, Aristides}, + TITLE = {On the tangent space of the deformation functor of curves with + automorphisms}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {1}, + YEAR = {2007}, + NUMBER = {2}, + PAGES = {119--161}, + ISSN = {1937-0652}, + MRCLASS = {14H37 (14B10 14D15)}, + MRNUMBER = {MR2361938}, +} +@article {newfamilyofmaximal, + AUTHOR = {Giulietti, Massimo and Korchm{\'a}ros, G{\'a}bor}, + TITLE = {A new family of maximal curves over a finite field}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {343}, + YEAR = {2009}, + NUMBER = {1}, + PAGES = {229--245}, + ISSN = {0025-5831}, + CODEN = {MAANA}, + MRCLASS = {14G15 (11G20 14H45)}, + MRNUMBER = {MR2448446}, + DOI = {10.1007/s00208-008-0270-z}, + URL = {http://dx.doi.org/10.1007/s00208-008-0270-z}, +} +@article {maxnotgalois, + AUTHOR = {Garcia, Arnaldo and Stichtenoth, Henning}, + TITLE = {A maximal curve which is not a {G}alois subcover of the + {H}ermitian curve}, + JOURNAL = {Bull. Braz. Math. Soc. (N.S.)}, + FJOURNAL = {Bulletin of the Brazilian Mathematical Society. New Series. + Boletim da Sociedade Brasileira de Matem\'atica}, + VOLUME = {37}, + YEAR = {2006}, + NUMBER = {1}, + PAGES = {139--152}, + ISSN = {1678-7544}, + MRCLASS = {11G20 (11D45)}, + MRNUMBER = {MR2223491 (2007a:11083)}, +MRREVIEWER = {Niko Naumann}, + DOI = {10.1007/s00574-006-0008-z}, + URL = {http://dx.doi.org/10.1007/s00574-006-0008-z}, +} + +@article {embedingmaximal, + AUTHOR = {Korchm{\'a}ros, G{\'a}bor and Torres, Fernando}, + TITLE = {Embedding of a maximal curve in a {H}ermitian variety}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {128}, + YEAR = {2001}, + NUMBER = {1}, + PAGES = {95--113}, + ISSN = {0010-437X}, + CODEN = {CMPMAF}, + MRCLASS = {11G20 (14G05 14G15)}, + MRNUMBER = {MR1847666 (2002i:11060)}, +MRREVIEWER = {Miriam D. Abd{\'o}n}, + DOI = {10.1023/A:1017553432375}, + URL = {http://dx.doi.org/10.1023/A:1017553432375}, +} + +@article {maximal:97, + AUTHOR = {Fuhrmann, Rainer and Garcia, Arnaldo and Torres, Fernando}, + TITLE = {On maximal curves}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {67}, + YEAR = {1997}, + NUMBER = {1}, + PAGES = {29--51}, + ISSN = {0022-314X}, + CODEN = {JNUTA9}, + MRCLASS = {11G20 (11R58 14G15)}, + MRNUMBER = {MR1485426 (98k:11077)}, +MRREVIEWER = {Gabriel D. Villa-Salvador}, + DOI = {10.1006/jnth.1997.2148}, + URL = {http://dx.doi.org/10.1006/jnth.1997.2148}, +} + +@article{KoANT, + author = {Kontogeorgis, Aristides I.}, + title = {The group of automorphisms of the function fields of the curve $x\sp n+y\sp m+1=0$}, + journal = {J. Number Theory}, + year = 1998, + volume = {72}, + number = 1, + pages = {110--136}, + file = {/home/kontogar/Papers/pdf/D1.pdf}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X} +} + + +@incollection{SMLE:97, + author = {de Smit, Bart and Lenstra, Jr., Hendrik W.}, + title = {Explicit construction of universal deformation rings}, + booktitle = {Modular forms and Fermat's last theorem (Boston, MA, 1995)}, + pages = {313--326}, + publisher = {Springer}, + year = {1997}, + address = {New York}, + mrclass = {11F80}, + mrnumber = {1 638 482} +} + + + +@article{Leopoldt:96, + author = {Leopoldt, Heinrich-Wolfgang}, + title = {\"{U}ber die {A}utomorphismengruppe des {F}ermatk\"orpers}, + journal = {J. Number Theory}, + year = 1996, + volume = {56}, + number = 2, + pages = {256--282}, + file = {/home/kontogar/Papers/pdf/LeopoldtNumth.pdf}, + abstract = {In this paper the full group of automorphisms of the curve x^n +y^n =z n over an +algebraically closed field of arbitrary characteristic p 0 is determined. It turns out +that in general the group is of order 6n 2 and of the structure known from +characteristic 0. However there are exceptional cases, namely characteristic p>0 +and exponent n=1+p h >3. In this case the automorphism group is the projective +unitary group PGU(3, q) (with q=ph ) of order (q 3 +1) q 3(q 2 &1). The proof +involves a detailed study of Weierstra? points in characteristic p>0. A character- +ization of the Fermat function fields in terms of their genus and their automorphism +group is given. 1996 Academic Press, Inc.}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X} +} + +@book{LiuBook, + author = {Liu, Qing}, + title = {Algebraic geometry and arithmetic curves}, + year = {2002}, + volume = {6}, + series = {Oxford Graduate Texts in Mathematics}, + address = {Oxford}, + note = {Translated from the French by Reinie Ern\'e, + Oxford Science Publications}, + isbn = {0-19-850284-2}, + mrclass = {14-01 (11G30 14A05 14A15 14Gxx 14Hxx)}, + mrnumber = {2003g:14001}, + mrreviewer = {C{\'{\i}}cero Fernandes de Carvalho}, + pages = {xvi+576}, + publisher = {Oxford University Press} +} + +@article{mumford-curves, + author = {Mumford, David}, + title = {An analytic construction of degenerating curves over complete + local rings}, + journal = {Compositio Math.}, + year = {1972}, + volume = {24}, + pages = {129--174}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {14H15}, + mrnumber = {MR0352105 (50 \#4592)}, + mrreviewer = {I. Dolgacev} +} + +@article{Matsumura:64, + author = {Matsumura, Hideyuki and Monsky, Paul}, + title = {On the automorphisms of hypersurfaces}, + journal = {J. Math. Kyoto Univ.}, + year = {1963/1964}, + volume = {3}, + pages = {347--361}, + +} + +@article {MatManusc, + AUTHOR = {Matignon, Michel}, + TITLE = {{$p$}-groupes ab\'eliens de type {$(p,\cdots,p)$} et disques + ouverts {$p$}-adiques}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {99}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {93--109}, + ISSN = {0025-2611}, + CODEN = {MSMHB2}, + MRCLASS = {14G32 (12F12)}, + MRNUMBER = {MR1697205 (2000e:14028)}, +MRREVIEWER = {Andy R. Magid}, +} + + +@article {MatignonGreen98, + AUTHOR = {Green, Barry and Matignon, Michel}, + TITLE = {Liftings of {G}alois covers of smooth curves}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {113}, + YEAR = {1998}, + NUMBER = {3}, + PAGES = {237--272}, + ISSN = {0010-437X}, + CODEN = {CMPMAF}, + MRCLASS = {14H30 (11G20 14D15 14E22)}, + MRNUMBER = {MR1645000 (99k:14045a)}, +MRREVIEWER = {Akio Tamagawa}, +} + + +@article{MazDef, + author = {Mazur, B.}, + title = {Deformation theory of {G}alois Representations + (in + {M}odular forms and {F}ermat's last theorem)}, + year = {1997}, + pages = {xx+582}, + note = {Papers from the Instructional Conference on Number Theory and + Arithmetic Geometry held at Boston University, Boston, MA, + August 9--18, 1995}, + address = {New York}, + editor = {Cornell, Gary and Silverman, Joseph H. and Stevens, Glenn}, + isbn = {0-387-94609-8; 0-387-98998-6}, + mrclass = {11-06 (11D41 11F80 11Fxx 11G05)}, + mrnumber = {99k:11004}, + mrreviewer = {M. Ram Murty}, + publisher = {Springer-Verlag} +} + +@article{Nak, + author = {Nakajima, Sh{\=o}ichi}, + title = {$p$-ranks and automorphism groups of algebraic curves}, + journal = {Trans. Amer. Math. Soc.}, + year = {1987}, + volume = {303}, + number = {2}, + pages = {595--607}, + coden = {TAMTAM}, + fjournal = {Transactions of the American Mathematical Society}, + issn = {0002-9947}, + mrclass = {14H30}, + mrnumber = {88h:14037}, + mrreviewer = {Jos{\'e} Felipe Voloch} +} + +@article{NakAbel, + author = {Nakajima, Sh{\=o}ichi}, + title = {On abelian automorphism groups of algebraic curves}, + journal = {J. London Math. Soc. (2)}, + year = {1987}, + volume = {36}, + number = {1}, + pages = {23--32}, + coden = {JLMSAK}, + fjournal = {Journal of the London Mathematical Society. Second Series}, + issn = {0024-6107}, + mrclass = {14H05}, + mrnumber = {MR897671 (88i:14016)}, + mrreviewer = {C. Maclachlan} +} + +@book{NeuCoho, + author = {Neukirch, J{\"u}rgen and Schmidt, Alexander and Wingberg, Kay}, + title = {Cohomology of number fields}, + year = {2000}, + volume = {323}, + series = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + address = {Berlin}, + isbn = {3-540-66671-0}, + mrclass = {11R34 (11-02 11G45 11R23 11S20 11S25 11S31 12G05)}, + mrnumber = {MR1737196 (2000j:11168)}, + mrreviewer = {Gabriel D. Villa-Salvador}, + pages = {xvi+699}, + publisher = {Springer-Verlag} +} + +@article{Noma:95, + author = {Noma, Atsushi}, + title = {Hypersurfaces with smooth dual varieties}, + journal = {Amer. J. Math.}, + year = {1995}, + volume = {117}, + number = {6}, + pages = {1507--1515}, + coden = {AJMAAN}, + fjournal = {American Journal of Mathematics}, + issn = {0002-9327}, + mrclass = {14J70 (14J60)}, + mrnumber = {97a:14046}, + mrrevr = {P. Abellanas} +} + + + +@book {ZariskiBo, + AUTHOR = {Zariski, Oscar and Samuel, Pierre}, + TITLE = {Commutative algebra. {V}ol. 1}, + NOTE = {With the cooperation of I. S. Cohen, + Corrected reprinting of the 1958 edition, + Graduate Texts in Mathematics, No. 28}, + PUBLISHER = {Springer-Verlag}, + ADDRESS = {New York}, + YEAR = {1975}, + PAGES = {xi+329}, + MRCLASS = {13-02}, + MRNUMBER = {MR0384768 (52 \#5641)}, +} + + +@article{Pries:02, + author = {Pries, Rachel J.}, + title = {Families of wildly ramified covers of curves}, + journal = {Amer. J. Math.}, + year = {2002}, + volume = {124}, + number = {4}, + pages = {737--768}, + coden = {AJMAAN}, + fjournal = {American Journal of Mathematics}, + issn = {0002-9327}, + mrclass = {14H30 (14E22)}, + mrnumber = {MR1914457 (2003i:14032)}, + mrreviewer = {Niels Borne} +} + +@article{Pries:04, + author = {Pries, Rachel J.}, + title = {Deformation of wildly ramified actions on curves}, + journal = {arXiv:math.AG}, + year = {2004}, + number = {0403056 v2}, + issn = {0002-9327}, + mrclass = {14H30 (14G22)} +} + +@article{Roq:70, + author = {Roquette, Peter}, + title = {Absch\"atzung der {A}utomorphismenanzahl von {F}unktionenk\"orpern bei {P}rimzahlcharakteristik}, + journal = {Math. Z.}, + year = {1970}, + volume = {117}, + pages = {157--163}, + mrclass = {14.35}, + mrnumber = {43 \#4826}, + mrreviewer = {F. Oort} +} + +@article {SeSu94, + AUTHOR = {Sekiguchi, Tsutomu and Suwa, Noriyuki}, + TITLE = {Th\'eories de {K}ummer-{A}rtin-{S}chreier-{W}itt}, + JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, + FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. + Math\'ematique}, + VOLUME = {319}, + YEAR = {1994}, + NUMBER = {2}, + PAGES = {105--110}, + ISSN = {0764-4442}, + CODEN = {CASMEI}, + MRCLASS = {14L15}, + MRNUMBER = {MR1288386}, +} + +@article {SeSu95, + AUTHOR = {Sekiguchi, Tsutomu and Suwa, Noriyuki}, + TITLE = {Th\'eorie de {K}ummer-{A}rtin-{S}chreier et applications}, + NOTE = {Les Dix-huiti\`emes Journ\'ees Arithm\'etiques (Bordeaux, + 1993)}, + JOURNAL = {J. Th\'eor. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux}, + VOLUME = {7}, + YEAR = {1995}, + NUMBER = {1}, + PAGES = {177--189}, + ISSN = {1246-7405}, + MRCLASS = {11R37 (14L15)}, + MRNUMBER = {MR1413576 (98d:11139)}, +MRREVIEWER = {Peter Stevenhagen}, +} + + + +@book{SeGalCoh, + author = {Serre, Jean-Pierre}, + title = {Galois cohomology}, + year = {1997}, + address = {Berlin}, + note = {Translated from the French by Patrick Ion and revised by the + author}, + isbn = {3-540-61990-9}, + mrclass = {12G05 (11R34)}, + mrnumber = {98g:12007}, + pages = {x+210}, + publisher = {Springer-Verlag} +} + +@book{SeL, + author = {Serre, Jean-Pierre}, + title = {Local fields}, + year = {1979}, + address = {New York}, + note = {Translated from the French by Marvin Jay Greenberg}, + isbn = {0-387-90424-7}, + mrclass = {12Bxx}, + mrnumber = {82e:12016}, + pages = {viii+241}, + publisher = {Springer-Verlag} +} + +@book{SerreTrees, + author = {Serre, Jean-Pierre}, + title = {Trees}, + year = {1980}, + address = {Berlin}, + note = {Translated from the French by John Stillwell}, + isbn = {3-540-10103-9}, + mrclass = {20H10 (05C05 22E50)}, + mrnumber = {MR607504 (82c:20083)}, + pages = {ix+142}, + publisher = {Springer-Verlag} +} + +@book{SGA:2, + author = {Grothendieck, Alexander}, + title = {Cohomologie locale des faisceaux coh\'erents et th\'eor\`emes + de {L}efschetz locaux et globaux $({S}{G}{A}$ $2)$}, + year = {1968}, + address = {Amsterdam}, + note = {Augment\'e d'un expos\'e par Mich\`ele Raynaud, + S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie, 1962, + Advanced Studies in Pure Mathematics, Vol. 2}, + pages = {vii+287}, + publisher = {North-Holland Publishing Co.} +} + +@book{SGA:7, + title = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. {I}{I}}, + year = {1973}, + address = {Berlin}, + note = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie + 1967--1969 (SGA 7 II), + Dirig\'e par P. Deligne et N. Katz, + Lecture Notes in Mathematics, Vol. 340}, + pages = {x+438}, + publisher = {Springer-Verlag} +} + +@article {KaGa, + AUTHOR = {Katz, Nicholas M.}, + TITLE = {Local-to-global extensions of representations of fundamental + groups}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {36}, + YEAR = {1986}, + NUMBER = {4}, + PAGES = {69--106}, + ISSN = {0373-0956}, + CODEN = {AIFUA7}, + MRCLASS = {14H30 (14B20 14E20)}, + MRNUMBER = {MR867916 (88a:14032)}, +MRREVIEWER = {Noriko Yui}, + URL = {http://www.numdam.org/item?id=AIF_1986__36_4_69_0}, +} + +@incollection{Shioda:87, + author = {Shioda, Tetsuji}, + title = {Arithmetic and geometry of {F}ermat curves}, + booktitle = {Algebraic Geometry Seminar (Singapore, 1987)}, + pages = {95--102}, + publisher = {World Sci. Publishing}, + year = {1988}, + address = {Singapore}, + +} +@book {Burrow, + AUTHOR = {Burrow, Martin}, + TITLE = {Representation theory of finite groups}, + NOTE = {Corrected reprint of the 1971 edition}, + PUBLISHER = {Dover Publications Inc.}, + ADDRESS = {New York}, + YEAR = {1993}, + PAGES = {viii+184}, + ISBN = {0-486-67487-8}, + MRCLASS = {20-01 (20Cxx)}, + MRNUMBER = {MR1218391 (94a:20001)}, +} + +@article{Sch, + author = {Schlessinger, Michael}, + title = {Functors of {A}rtin rings}, + journal = {Trans. Amer. Math. Soc.}, + year = {1968}, + volume = {130}, + pages = {208--222}, + mrclass = {14.55}, + mrnumber = {36 \#184}, + mrreviewer = {M. Miyanishi} +} + +@book{StiBo, + author = {Stichtenoth, Henning}, + title = {Algebraic function fields and codes}, + year = {1993}, + address = {Berlin}, + isbn = {3-540-56489-6}, + mrclass = {14H05 (11R58 11T71 14G15 94B27)}, + mrnumber = {94k:14016}, + mrreviewer = {R. F. Lax}, + pages = {x+260}, + publisher = {Springer-Verlag} +} + +@article{StiI, + author = {Stichtenoth, Henning}, + title = {\"{U}ber die {A}utomorphismengruppe eines algebraischen {F}unktionenk\"orpers von {P}rimzahlcharakteristik. {I}. {E}ine {A}bsch\"atzung der {O}rdnung der {A}utomorphismengruppe}, + journal = {Arch. Math. (Basel)}, + year = 1973, + volume = {24}, + pages = {527--544}, + file = {/home/kontogar/Papers/pdf/StichtenothI.pdf}, + mrclass = {14H05}, + mrnumber = {49 \#2749}, + mrreviewer = {W.-D. Geyer} +} + +@article{StiII, + author = {Stichtenoth, Henning}, + title = {\"{U}ber die {A}utomorphismengruppe eines algebraischen {F}unktionenk\"orpers von {P}rimzahlcharakteristik. {II}. {E}in spezieller {T}yp von {F}unktionenk\"orpern}, + journal = {Arch. Math. (Basel)}, + year = 1973, + volume = {24}, + pages = {615--631}, + file = {/home/kontogar/Papers/pdf/stichII.pdf}, + mrclass = {14H05}, + mrnumber = {53 \#8068}, + mrreviewer = {W.-D. Geyer} +} + +@article{Subrao, + author = {Subrao, Dor{\'e}}, + title = {The {$p$}-rank of {A}rtin-{S}chreier curves}, + journal = {Manuscripta Math.}, + year = 1975, + volume = {16}, + number = 2, + pages = {169--193}, + file = {/home/kontogar/Papers/pdf/Caartier.pdf}, + fjournal = {Manuscripta Mathematica}, + issn = {0025-2611}, + mrclass = {14H45 (14H30)}, + mrnumber = {MR0376693 (51 \#12868)}, + mrreviewer = {K. Kiyek} +} +@book {Atiyah, + AUTHOR = {Atiyah, M. F. and Macdonald, I. G.}, + TITLE = {Introduction to commutative algebra}, + PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don + Mills, Ont.}, + YEAR = {1969}, + PAGES = {ix+128}, + MRCLASS = {13.00}, + MRNUMBER = {MR0242802 (39 \#4129)}, +MRREVIEWER = {J. A. Johnson}, +} + +@article{Tze:95, + author = {Tzermias, Pavlos}, + title = {The group of automorphisms of the {F}ermat curve}, + journal = {J. Number Theory}, + year = {1995}, + volume = {53}, + number = {1}, + pages = {173--178}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X} +} + +@incollection{Ful-Laz:80, + author = {Fulton, William and Lazarsfeld, Robert}, + title = {Connectivity and its applications in algebraic geometry}, + booktitle = {Algebraic geometry (Chicago, Ill., 1980)}, + pages = {26--92}, + publisher = {Springer}, + year = {1981}, + address = {Berlin}, + +} + +@article{Val-Mad:80, + author = {Valentini, Robert C. and Madan, Manohar L.}, + title = {A {H}auptsatz of {L}. {E}. {D}ickson and {A}rtin-{S}chreier + extensions}, + journal = {J. Reine Angew. Math.}, + year = {1980}, + volume = {318}, + pages = {156--177}, + coden = {JRMAA8}, + fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, + issn = {0075-4102}, + mrclass = {12F20}, + mrnumber = {82e:12030}, + mrrevr = {Sudesh Khanduja} +} + +@book{Weiss, + author = {Weiss, Edwin}, + title = {Cohomology of groups}, + year = {1969}, + address = {New York}, + mrclass = {18.20 (10.68)}, + mrnumber = {41 \#8499}, + mrreviewer = {J. V. Armitage}, + pages = {x+274}, + publisher = {Academic Press} +} + +@book{Weibel1, + author = {Weibel, Charles A.}, + title = {An {I}ntroduction to {H}omological {A}lgebra}, + year = {1994}, + address = {Cambridge}, + isbn = {0-521-43500-5; 0-521-55987-1}, + mrclass = {18-01 (16-01 17-01 20-01 55Uxx)}, + mrnumber = {95f:18001}, + mrreviewer = {Kenneth A. Brown}, + pages = {xiv+450}, + publisher = {Cambridge University Press} +} +@book {ShafaBo1, + AUTHOR = {Shafarevich, Igor R.}, + TITLE = {Basic algebraic geometry. 1}, + EDITION = {Second}, + NOTE = {Varieties in projective space, + Translated from the 1988 Russian edition and with notes by + Miles Reid}, + PUBLISHER = {Springer-Verlag}, + ADDRESS = {Berlin}, + YEAR = {1994}, + PAGES = {xx+303}, + ISBN = {3-540-54812-2}, + MRCLASS = {14-01}, + MRNUMBER = {MR1328833 (95m:14001)}, +} +@article{wpsurvey, + author = {Eun--Ju Kang}, + title = {ON WEIERSTRASS POINTS, available at http://mathnet.kaist.ac.kr/}, + journal = {Trends in Mathematics}, + year = {1999}, + volume = {2}, + pages = {124--128}, + mrnumber= {} +} +@article {GScurve, + AUTHOR = {Garcia, Arnaldo and Stichtenoth, Henning}, + TITLE = {A maximal curve which is not a {G}alois subcover of the + {H}ermitian curve}, + JOURNAL = {Bull. Braz. Math. Soc. (N.S.)}, + FJOURNAL = {Bulletin of the Brazilian Mathematical Society. New Series. + Boletim da Sociedade Brasileira de Matem\'atica}, + VOLUME = {37}, + YEAR = {2006}, + NUMBER = {1}, + PAGES = {139--152}, + ISSN = {1678-7544}, + MRCLASS = {11G20 (11D45)}, + MRNUMBER = {MR2223491 (2007a:11083)}, +MRREVIEWER = {Niko Naumann}, + DOI = {10.1007/s00574-006-0008-z}, + URL = {http://dx.doi.org/10.1007/s00574-006-0008-z}, +} + +@article{Fieldsofmoduli, + author = {Kontogeorgis, Aristides}, + title = {Field of moduli versus field of definition for cyclic covers of the projective line, preprint, available at http://myria.math.aegean.gr/kontogar/papers.html}, + year = {2008}, + address = {}, + isbn = {}, + mrclass = {}, + mrnumber = {}, + mrreviewer = {}, + pages = {}, + mrnumber = {} +} +@article{chiniseman, + author = {Qingquan Wu and Renate Scheidler}, + title = {The Ramification Groups And Different Of a Compositum of Artin-Shreier Extensions, preprint, available at http://math.ucalgary.ca/~quwu/ram-groups.pdf}, + year = {2010}, + address = {}, + isbn = {}, + mrclass = {}, + mrnumber = {}, + mrreviewer = {}, + pages = {}, + +} +@book {SalvadorBook, + AUTHOR = {Villa Salvador, Gabriel Daniel}, + TITLE = {Topics in the theory of algebraic function fields}, + SERIES = {Mathematics: Theory \& Applications}, + PUBLISHER = {Birkh\"auser Boston Inc.}, + ADDRESS = {Boston, MA}, + YEAR = {2006}, + PAGES = {xviii+652}, + ISBN = {978-0-8176-4480-2; 0-8176-4480-6}, + MRCLASS = {11-02 (11R32 11R58 11S20 94A60)}, + MRNUMBER = {MR2241963 (2007i:11002)}, +MRREVIEWER = {Manfred Lochter}, +} + + +@article{AntonKont2006, + author = {Antoniadis, Jannis A. and Kontogeorgis, Aristides}, + title = {On cyclic covers of the projective line}, + journal = {Manuscripta Math.}, + year = 2006, + volume = {121}, + number = 1, + pages = {105--130}, + file = {/home/kontogar/Papers/pdf/manuscripta.pdf}, + abstract = {Abstract. We construct configuration spaces for cyclic covers of the projective line that +admit extra automorphisms and we describe the locus of curves with given automorphism +group. As an application we provide examples of arbitrary high genus that are defined over +their field of moduli and are not hyperelliptic.}, + coden = {MSMHB2}, + fjournal = {Manuscripta Mathematica}, + issn = {0025-2611}, + mrclass = {14H30 (14H10)}, + mrnumber = {MR2258533 (2007f:14025)}, + mrreviewer = {Tanush Shaska} +} + +@book{Connes1994, + author = {Connes, Alain}, + title = {Noncommutative geometry}, + year = 1994, + address = {San Diego, CA}, + file = {/home/kontogar/Papers/pdf/connes.pdf}, + comment = {FEATURED REVIEW. + + + + Alain Connes received the Fields Medal at the Warsaw Congress in 1983. The citation, which concentrates on his work on von Neumann algebras, mentions noncommutative geometry in passing, and states confidently that "the subject will rapidly develop much further". This large (over 600 pages), dense, fascinating, and beautiful book is evidence of the accuracy of this prognosis. + + To see what is meant by the phrase "noncommutative geometry", consider ordinary geometry: for example, the geometry of a surface $S$ in three-dimensional Euclidean space $R^3$. Following Descartes, we study the geometry of $S$ using coordinates. These are just three functions $x$, $y$, $z$ on $R^3$, and their restrictions to $S$ generate, in an appropriate sense, the algebra $C(S)$ of all continuous functions on $S$. All the geometry of $S$ is encoded in this algebra $C(S)$; in fact, the points of $S$ can be recovered simply as the algebra homomorphisms from $C(S)$ to C. In the language of physics, one might say that the transition from $S$ to $C(S)$ is a transition from a "particle picture" to a "field picture" of the same physical situation. + + One notes that the algebra $C(S)$ appearing here is commutative. It is therefore natural to suggest that it might be valuable to think of noncommutative algebras in geometric terms, as the algebras of functions on "noncommutative spaces". Some attempts in this direction have been made from algebraic geometry, but Connes's program rests on differential geometry and incorporates deep techniques from functional analysis. Motivation for this program comes from a number of sources. One is physics: quantum mechanics asserts that physical observables such as position and momentum should be modeled by elements of a noncommutative algebra. Another is a series of examples showing that objects such as the space of (unitary) representations of a group, or the space of leaves of a foliation, may be most appropriately modeled as noncommutative spaces. A third comes from the application of $K$-theory to operator algebras and the link (in the case of group $C^*$-algebras) to the Novikov higher-signature conjecture and +surgery theory. All these together with other motivations and applications are discussed in detail in the book. + + Connes's book guides the reader through the appropriate noncommutative versions of four successively more refined kinds of geometric structure: measure theory, topology (including algebraic topology), differential topology (manifold theory), and differential (Riemannian) geometry. To begin with the coarsest of these, noncommutative measure theory means the theory of von Neumann algebras. Let $H$ be a Hilbert space, $B(H)$ the set of bounded linear operators on it. A von Neumann algebra is an involutive subalgebra $A$ of $B(H)$ which is closed in the weak topology on $B(H)$. The commutative example to keep in mind is $H=L^2(X,µ)$, where $(X,µ)$ is a measure space, and $A=L^\infty(X,µ)$ acting by multiplication; the weak topology coincides with the topology of pointwise almost everywhere convergence on bounded sets. This algebra is in a natural sense a "direct integral" of copies of $C$, which is a factor---that is, a von Neumann algebra with trivial centre. Already in the original papers of Murray and von +Neumann one finds the classification of factors into three types: type I, matrix algebras; type II, admitting a "continuous dimension" function with real values; type III, admitting no dimension function. Of these, the factors of type III are the most mysterious. Much of Connes's early work was devoted to elucidating their structure, and this is described in Chapter V of the book. This chapter also contains a discussion of the work of Vaughan Jones on subfactors of factors of type II, which had such remarkable applications to knot theory. + + An example which is significant for many aspects of the book comes from the theory of foliations. Let $(V,{\scr F})$ be a compact foliated manifold. We want to study the "space of leaves" $V/{\scr F}$---initially only as a measure space, but then successively in the more refined categories mentioned above. If the foliation is ergodic---think of the irrational-slope flow on a torus---then the quotient measure space in the usual sense is trivial. But we can form a noncommutative von Neumann algebra whose elements are measurable families of operators on the $L^2$ spaces of the leaves of the foliations, and it turns out that this von Neumann algebra is equivalent in the non-singular case to the one arising from the usual measure-theoretic quotient, and that it is interesting even in the singular case; for instance, the von Neumann algebra of the irrational-slope flow is of type II, and its "continuous dimension" function is given by the unique invariant transverse measure on the foliation. There are remarkable +links between this von Neumann algebra and the more classical invariants of foliations, for example the result (originally due to Steve Hurder) that if the Godbillon-Vey class of a foliation is nonzero, then the associated von Neumann algebra is of type III. + + The noncommutative analogue of topology depends on the theory of $C^*$-algebras. These are involutive subalgebras of $B(H)$ which are closed for the norm topology: the standard (in fact, the only) commutative example is the algebra of continuous functions vanishing at infinity on a locally compact Hausdorff space. The noncommutative quotient construction can be applied in the $C^*$-algebraic setting also. An example of particular interest arises by applying the quotient construction to the trivial action of a discrete group $\Gamma$ on a point; one obtains the (reduced) group $C^*$-algebra $C^*_r(\Gamma)$, which may be regarded as an analytical completion of the group algebra $C\Gamma$. Connections with geometric topology arise when $\Gamma$ is the fundamental group of a manifold. + + By the theorem of Gel\cprime fand and Na\u\i mark, the study of commutative $C^*$-algebras is exactly the same as the study of locally compact Hausdorff spaces. It is natural therefore to ask whether the tools of algebraic topology extend to the noncommutative $C^*$-algebraic world. It turns out that topological $K$-theory and its $S$-dual theory, $K$-homology, have natural extensions to the category of $C^*$-algebras. Moreover, there is a natural relationship with index theory in the case of $C^*$-algebras arising from the noncommutative quotient construction. Recall that Atiyah and Singer showed that the index of a family of elliptic operators over a base $B$ should be thought of as an element of the $K$-theory group $K^*(B)$. Analogously, a family of elliptic operators along the leaves of a foliation, or on the fibres of any other quotient, has an index in the $K$-theory of the noncommutative quotient $C^*$-algebra. A very general conjecture is then that the whole $C^*$-algebra $K$-theory group is +exactly generated by indices of this kind. This is known as the Baum-Connes conjecture, and it has been verified in a large number of different situations. It also has noteworthy implications: for example, the Baum-Connes conjecture for a discrete group $\Gamma$ implies the Novikov conjecture for $\Gamma$, which (via surgery theory) is crucial to the topology of high-dimensional manifolds having $\Gamma$ as fundamental group. + + Chapter II of the book contains a detailed account of this material. The general theory is illustrated with many beautiful examples. Connes gives particular prominence to groupoids arising from geometric situations, and the $K$-theory maps arising from associated deformations of algebras. For example, the tangent groupoid is an algebraic encoding of the idea that the tangent bundle of a manifold $M$ can be obtained by blowing up the diagonal in $M\times M$; the associated convolution algebra encapsulates the index-theoretic aspects of the pseudodifferential calculus. + + The next stage in the development is the noncommutative analogue of differential topology. Granted that $K$-theories seem to be "natural" (co)homology theories in the noncommutative category, one might still search for a noncommutative analogue of ordinary (co)homology. The strategy in the search for the noncommutative analogue of some notion is first to find a way of formulating the commutative notion in "function" rather than "point" terms, and then to try replacing the functions by elements of a noncommutative algebra. Now the version of cohomology that is most naturally expressed in "function" terms is de Rham cohomology, but (since it involves differentiation) it must be formulated in terms of the dense subalgebra of smooth functions inside the $C^*$-algebra of continuous ones. In the absence of a general smoothing theory for $C^*$-algebras (as there is, say, for high-dimensional topological manifolds) the choice of such a subalgebra has to be made ad hoc. Often, however, a natural such subalgebra is +available, and one refers to it as a smooth structure on the $C^*$-algebra in question. + + Suppose a smooth structure has been chosen. How should we construct "noncommutative de Rham theory"? Connes's answer is his theory of cyclic cohomology, expounded in Chapter III of the book. Cyclic cohomology has received an extensive purely algebraic development in recent years \ref[see, for example, J.-L. Loday, Cyclic homology, Springer, Berlin, 1992; MR1217970 (94a:19004)], but Connes's discussion remains close to the original geometric motivation. One of the deepest applications is to the construction of the transverse fundamental class for a foliation: this is a map from the $K$-theory of the "transverse space" to the real numbers, and it would have an easy construction if there were an invariant transverse Riemannian metric. In general no such metric can be found, but Connes noticed that this problem was analogous to one that he had already surmounted in his work on factors of type III. Following this insight, and combining ideas from cyclic theory (here the choice of an appropriate dense subalgebra +is a very delicate matter) and sophisticated versions of the Thom isomorphism in $K$-theory, Connes was able to construct the desired map. Geometric results about foliations, including the theorem of Hurder mentioned above, are immediate corollaries. + + A second motivation for cyclic cohomology, equally significant, is the idea of "quantized calculus", expounded in Connes's Chapter IV. If $A$ is an algebra of operators on some Hilbert space $H$, and $F$ an operator on $H$ with $F^2=1$, then the definition $da = [F,a] = Fa - aF$ obeys the basic rule $d^2=0$ of de Rham theory. If in addition $F$ and $A$ are "almost commuting" enough that any product of sufficiently many commutators $[F,a]$ is of trace class, then the trace can be used to define an "integral" of these "differential forms" and we have the ingredients for a "noncommutative de Rham current", i.e. a cyclic cocycle. A helpful example is $A=C^\infty(M)$, $M$ a compact manifold of dimension $n$, and $F$ some (zeroth order) pseudodifferential involution. The commutators are then pseudodifferential operators of order $-1$, and any product of more than $n$ of them is therefore trace-class. In this example we see that the notion of dimension in quantized calculus is related to the "degree of +traceability" of certain commutators. + + Not all cyclic classes arise in this way. In fact, such a cyclic class belongs to the image of a "Chern character" map from $K$-homology. It follows, therefore, that if such a cyclic class is paired with an element of $K$-theory the result must be an integer, because the evaluation of pairing between $K$-theory and $K$-homology ultimately reduces to the computation of a Fredholm index. In this way one obtains integrality results somewhat analogous to those provided by the Atiyah-Singer index theorem. An application discussed in detail by Connes is the work of J. Bellissard on the existence of integer plateaux of conductivity in the quantum Hall effect. This concerns the flow of electricity in a crystal subjected to electric and magnetic fields. In general, the "natural" observables in this problem generate an algebra isomorphic to that associated to the irrational-slope foliation on a torus, and the integrality arises from an associated cyclic 2-cocycle. + + The last chapter in the book is entitled "The metric aspect of noncommutative geometry", and begins an investigation of the analogue of Riemannian geometry and Yang-Mills theory in the noncommutative context. Many readers will focus with particular interest on the interpretation of the Standard Model of particle physics in terms of a noncommutative space which is the product of an ordinary manifold with a (very small) discrete space. Connes writes: "Our contribution should be regarded as an interpretation, of a geometric nature, of all the intricacies of the most accurate phenomenological model of high-energy physics.$\,\ldots$ It does undoubtedly confirm that high-energy physics is in fact unveiling the fine structure of space-time. Finally, it gives a status to the Higgs boson as just another gauge field, but one corresponding to a finite difference rather than a differential." + + The book is magnificently produced, and contains so much new material that it completely supersedes the French edition \ref[ G\'eom\'etrie non commutative, InterEditions, Paris, 1990; MR1079062 (92e:58016)]. The depth and variety of Connes' thought will lead the serious reader to explore the background and proofs of the results in more detail, and he or she will find a comprehensive bibliography for this purpose. + + On the back cover, the publishers describe the book as "the definitive treatment", but the subject is still developing so rapidly that the sense of finality conveyed by this phrase hardly seems appropriate. Vaughan Jones' comment, also on the cover, is more apt: "A milestone for mathematics". + +Reviewed by John Roe}, + isbn = {0-12-185860-X}, + mrclass = {46Lxx (19K56 22D25 58B30 58G12 81T13 81V22 81V70)}, + mrnumber = {MR1303779 (95j:46063)}, + mrreviewer = {John Roe}, + pages = {xiv+661}, + publisher = {Academic Press Inc.} +} + +@article{Anuradha2005, + author = {Anuradha, N.}, + title = {Zeta function of the projective curve {$aY\sp {2l}=bX\sp {2l}+cZ\sp {2l}$} over a class of finite fields, for odd primes {$l$}}, + journal = {Proc. Indian Acad. Sci. Math. Sci.}, + year = 2005, + volume = {115}, + number = 1, + pages = {1--14}, + file = {/home/kontogar/Papers/pdf/anhurada.ref}, + fjournal = {Indian Academy of Sciences. Proceedings. Mathematical Sciences}, + issn = {0253-4142}, + mrclass = {11G20 (14G10)}, + mrnumber = {MR2120596 (2006b:11061)}, + mrreviewer = {Niko Naumann} +} + +@article{Kleiman1974, + author = {Kleiman, Steven L. and Laksov, Dan}, + title = {Another proof of the existence of special divisors}, + journal = {Acta Math.}, + year = 1974, + volume = {132}, + pages = {163--176}, + file = {/home/kontogar/Papers/pdf/kleiman-laksov.pdf}, + fjournal = {Acta Mathematica}, + issn = {0001-5962}, + mrclass = {14C20 (14H99)}, + mrnumber = {MR0357398 (50 \#9866)}, + mrreviewer = {Guerino Mazzola} +} + +@article{GarciaSticht1991, + author = {Garc{\'{\i}}a, Arnaldo and Stichtenoth, Henning}, + title = {Elementary abelian {$p$}-extensions of algebraic function fields}, + journal = {Manuscripta Math.}, + year = 1991, + volume = {72}, + number = 1, + pages = {67--79}, + file = {/media/KINGSTON/Papers/pdf/GarciaStichtenoth.pdf}, + comment = {Let $F/K$ be an algebraic function field in one variable of characteristic $p>0$. The authors study Artin-Schreier extensions of $F$, i.e., extensions $E/F$ generated by an element $y$ with minimal equation $y^{p^n}-y=z$. If $K$ is finite then there are many fields of this kind having the maximum number $N(E)$ of rational places allowed by Weil's bound, but the authors show that for a fixed function field $F$ the number $N(E)$ is "asymptotically bad", i.e., for any sequence of extensions $E^{(j)}/F$ such as above with genus $g(E^{(j)})$ we have that if $[E^{(j)}:F]$ goes to infinity then $N(E^{(j)})/g(E^{(j)})$ goes to zero (Theorem 3.1). In the course of the proof they need to compute genera of intermediate function fields; this is done using methods of Hasse (Proposition 2.2; see also the proof of Theorem 3.1) and of Kani (Theorem 2.1; the resulting formula is very interesting). In the last section the authors give a family of fields of this kind which are nonclassical, i.e., fields all of +whose canonical Weierstrass gap sequences differ from $1,\cdots,g(E)$.}, + coden = {MSMHB2}, + fjournal = {Manuscripta Mathematica}, + issn = {0025-2611}, + mrclass = {11R58 (14H05)}, + mrnumber = {MR1107453 (92j:11139)}, + mrreviewer = {Paulo Viana} +} + +@book{Kodaira2005, + author = {Kodaira, Kunihiko}, + title = {Complex manifolds and deformation of complex structures}, + year = 2005, + series = {Classics in Mathematics}, + address = {Berlin}, + edition = {English}, + note = {Translated from the 1981 Japanese original by Kazuo Akao}, + file = {/home/kontogar/Papers/pdf/Kodaira K. Complex manifolds and deformation of complex structures (Springer 1986)(L)(T)(237s).djvu}, + isbn = {3-540-22614-1}, + mrclass = {32G05 (32-02)}, + mrnumber = {MR2109686 (2005h:32030)}, + pages = {x+465}, + publisher = {Springer-Verlag} +} + +@article{BeMe2002, + author = {Bertin, Jos{\'e} and M{\'e}zard, Ariane}, + title = {{ + Induction and Restriction In Formal Deformation of Coverings}}, + journal = {arXiv:math.AG/0205228}, + +} + +@book{BourbakiComm, + author = {Bourbaki, Nicolas}, + title = {Commutative {A}lgebra. {C}hapters 1--7}, + year = {1989}, + series = {Elements of Mathematics (Berlin)}, + address = {Berlin}, + note = {Translated from the French, + Reprint of the 1972 edition}, + isbn = {3-540-19371-5}, + mrclass = {13-XX (00A05)}, + mrnumber = {MR979760 (90a:13001)}, + pages = {xxiv+625}, + publisher = {Springer-Verlag} +} + +@article{Green-Mat-errata, + title = {Errata: ``{L}iftings of {G}alois covers of smooth curves'' + [{C}ompositio {M}ath. {\bf 113} (1998), no. 3, 237--272; + {MR}1645000 (99k:14045a)] by {B}.\ {G}reen and + {M}.\ {M}atignon}, + journal = {Compositio Math.}, + year = {1999}, + volume = {116}, + number = {2}, + pages = {239}, + coden = {CMPMAF}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {14H30 (11G20 14D15 14E22)}, + mrnumber = {MR1686844 (99k:14045b)}, + mrreviewer = {Akio Tamagawa} +} + +@article{Green-Mat, + author = {Green, Barry and Matignon, Michel}, + title = {Liftings of {G}alois covers of smooth curves}, + journal = {Compositio Math.}, + year = {1998}, + volume = {113}, + number = {3}, + pages = {237--272}, + coden = {CMPMAF}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {14H30 (11G20 14D15 14E22)}, + mrnumber = {MR1645000 (99k:14045a)}, + mrreviewer = {Akio Tamagawa} +} + +@article{NakT, + author = {Nakayama, Tadasi}, + title = {\"{U}ber die {B}eziehungen zwischen den {F}aktorensystemen und + der {N}ormklassengruppe eines galoisschen + {E}rweiterungsk\"orpers}, + journal = {Math. Ann.}, + year = {1936}, + volume = {112}, + number = {1}, + pages = {85--91}, + coden = {MAANA}, + fjournal = {Mathematische Annalen}, + issn = {0025-5831}, + mrclass = {Contributed Item}, + mrnumber = {MR1513037} +} + +@article{Bennama98, + author = {Bennama, H.}, + title = {Base de diff\'erentielles de premi\`ere esp\`ece des courbes + {$y\sp q=\prod\sp p\sb {i=0}(x-a\sb i)\sp {\alpha\sb i}$}: + application aux points de {W}eierstrass}, + journal = {J. Algebra}, + year = {1998}, + volume = {203}, + number = {1}, + pages = {261--269}, + coden = {JALGA4}, + fjournal = {Journal of Algebra}, + issn = {0021-8693}, + mrclass = {30F30 (14H55)}, + mrnumber = {MR1620666 (99c:30075)}, + mrreviewer = {Colin Stahlke} +} + +@article{bhugginsA, + author = {Bonnie Huggins}, + title = {Fields of Moduli of Hyperelliptic curves}, + journal = {Math. Res. Lett.}, + year = {2007}, + volume = {14}, + number = {00}, + pages = {10001--10014}, + +} + +@book{cohenfrey, + title = {Handbook of elliptic and hyperelliptic curve cryptography}, + year = {2006}, + editor = {Cohen, Henri and Frey, Gerhard and Avanzi, Roberto and Doche, + Christophe and Lange, Tanja and Nguyen, Kim and Vercauteren, + Frederik}, + series = {Discrete Mathematics and its Applications (Boca Raton)}, + isbn = {978-1-58488-518-4; 1-58488-518-1}, + mrclass = {94A60 (11T71 14G50 94-00)}, + mrnumber = {MR2162716}, + pages = {xxxiv+808}, + publisher = {Chapman \& Hall/CRC, Boca Raton, FL} +} + +@article{DebesDouai97, + author = {D{\`e}bes, Pierre and Douai, Jean-Claude}, + title = {Algebraic covers: field of moduli versus field of definition}, + journal = {Ann. Sci. \'Ecole Norm. Sup. (4)}, + year = {1997}, + volume = {30}, + number = {3}, + pages = {303--338}, + coden = {ASENAH}, + fjournal = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. + Quatri\`eme S\'erie}, + issn = {0012-9593}, + mrclass = {11G25 (11G20 12F12 14E20 14G20 14H30)}, + mrnumber = {MR1443489 (98k:11081)}, + mrreviewer = {Katherine F. Stevenson} +} + +@article{DebesEmsalem, + author = {D{\`e}bes, Pierre and Emsalem, Michel}, + title = {On fields of moduli of curves}, + journal = {J. Algebra}, + year = {1999}, + volume = {211}, + number = {1}, + pages = {42--56}, + coden = {JALGA4}, + fjournal = {Journal of Algebra}, + issn = {0021-8693}, + mrclass = {14H25 (14H30)}, + mrnumber = {MR1656571 (99k:14044)}, + mrreviewer = {Helmut V{\"o}lklein} +} + +@incollection{GeerECM00, + author = {van der Geer, Gerard}, + title = {Curves over finite fields and codes}, + booktitle = {European Congress of Mathematics, Vol. II (Barcelona, 2000)}, + pages = {225--238}, + publisher = {Birkh\"auser}, + year = {2001}, + volume = {202}, + series = {Progr. Math.}, + address = {Basel}, + mrclass = {14G50 (11G20 94A60)}, + mrnumber = {MR1905363 (2003g:14036)}, + mrreviewer = {San Ling} +} + +@article{Hasse34, + author = {Hasse, Helmut}, + title = {Theorie der relativ-zyklischen algebraischen {F}unktionenk\"orper, insbesondere bei endlichem {K}onstantenk\"orper}, + journal = {J. Reine Angew. Math.}, + year = {1934}, + volume = {172}, + pages = {37-54}, + issn = {0075-4102} +} + +@article{Kedlaya01, + author = {Kedlaya, Kiran S.}, + title = {Counting points on hyperelliptic curves using + {M}onsky-{W}ashnitzer cohomology}, + journal = {J. Ramanujan Math. Soc.}, + year = {2001}, + volume = {16}, + number = {4}, + pages = {323--338}, + fjournal = {Journal of the Ramanujan Mathematical Society}, + issn = {0970-1249}, + mrclass = {14G05 (11G25 14F43 14G15)}, + mrnumber = {MR1877805 (2002m:14019)}, + mrreviewer = {Miriam D. Abd{\'o}n} +} + +@article{kock04, + author = {K{\"o}ck, Bernhard}, + title = {Belyi's theorem revisited}, + journal = {Beitr\"age Algebra Geom.}, + year = {2004}, + volume = {45}, + number = {1}, + pages = {253--265}, + fjournal = {Beitr\"age zur Algebra und Geometrie. Contributions to Algebra + and Geometry}, + issn = {0138-4821}, + mrclass = {14H30 (12F10 14H25)}, + mrnumber = {MR2070647 (2005j:14036)}, + mrreviewer = {R{\u{a}}zvan Li{\c{t}}canu} +} + +@article{Ko:99, + author = {Kontogeorgis, Aristides}, + title = {The group of automorphisms of cyclic extensions of rational + function fields}, + journal = {J. Algebra}, + year = {1999}, + volume = {216}, + number = {2}, + pages = {665--706}, + coden = {JALGA4}, + fjournal = {Journal of Algebra}, + issn = {0021-8693}, + mrclass = {12F20 (20B25)}, + mrnumber = {MR1692965 (2000f:12005)}, + mrreviewer = {Ivan D. Chipchakov} +} + +@article{Lewittes63, + author = {Lewittes, Joseph}, + title = {Automorphisms of compact {R}iemann surfaces}, + journal = {Amer. J. Math.}, + year = {1963}, + volume = {85}, + pages = {734--752}, + fjournal = {American Journal of Mathematics}, + issn = {0002-9327}, + mrclass = {30.45 (14.20)}, + mrnumber = {MR0160893 (28 \#4102)}, + mrreviewer = {G. Springer} +} + +@article{Mazur73, + author = {Mazur, Barry}, + title = {Notes on \'etale cohomology of number fields}, + journal = {Ann. Sci. \'Ecole Norm. Sup. (4)}, + year = {1973}, + volume = {6}, + pages = {521--552 (1974)}, + fjournal = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. + Quatri\`eme S\'erie}, + issn = {0012-9593}, + mrclass = {14F20 (12B25)}, + mrnumber = {MR0344254 (49 \#8993)}, + mrreviewer = {Gerhard Pfister} +} + +@article{Morishita02, + author = {Morishita, Masanori}, + title = {On certain analogies between knots and primes}, + journal = {J. Reine Angew. Math.}, + year = {2002}, + volume = {550}, + pages = {141--167}, + coden = {JRMAA8}, + fjournal = {Journal f\"ur die Reine und Angewandte Mathematik}, + issn = {0075-4102}, + mrclass = {57M25 (11R32)}, + mrnumber = {MR1925911 (2003k:57008)}, + mrreviewer = {Jonathan A. Hillman} +} + +@article{MorrisonPinkham, + author = {Morrison, Ian and Pinkham, Henry}, + title = {Galois {W}eierstrass points and {H}urwitz characters}, + journal = {Ann. of Math. (2)}, + year = {1986}, + volume = {124}, + number = {3}, + pages = {591--625}, + coden = {ANMAAH}, + fjournal = {Annals of Mathematics. Second Series}, + issn = {0003-486X}, + mrclass = {14H30 (14F07)}, + mrnumber = {MR866710 (88a:14033)}, + mrreviewer = {R. F. Lax} +} + +@article{Reznikov97, + author = {Reznikov, Alexander}, + title = {Three-manifolds class field theory (homology of coverings for + a nonvirtually {$b\sb 1$}-positive manifold)}, + journal = {Selecta Math. (N.S.)}, + year = {1997}, + volume = {3}, + number = {3}, + pages = {361--399}, + coden = {SMATF6}, + fjournal = {Selecta Mathematica. New Series}, + issn = {1022-1824}, + mrclass = {57N10 (11R99 20J06)}, + mrnumber = {MR1481134 (99b:57041)}, + mrreviewer = {Darryl McCullough} +} + +@article{SchertzEnge, + author = {Enge, Andreas and Schertz, Reinhard}, + title = {Constructing elliptic curves over finite fields using double + eta-quotients}, + journal = {J. Th\'eor. Nombres Bordeaux}, + year = {2004}, + volume = {16}, + number = {3}, + pages = {555--568}, + fjournal = {Journal de Th\'eorie des Nombres de Bordeaux}, + issn = {1246-7405}, + mrclass = {11G15 (11G05 11G20 14K22)}, + mrnumber = {MR2144957 (2006d:11063)}, + mrreviewer = {Joseph H. Silverman} +} + +@incollection{shaska03, + author = {Shaska, T.}, + title = {Computational aspects of hyperelliptic curves}, + booktitle = {Computer mathematics}, + pages = {248--257}, + publisher = {World Sci. Publ., River Edge, NJ}, + year = {2003}, + volume = {10}, + series = {Lecture Notes Ser. Comput.}, + mrclass = {14H37 (14Q05)}, + mrnumber = {MR2061839 (2005h:14073)}, + mrreviewer = {Aristides I. Kontogeorgis} +} + +@article{Shimura72, + author = {Shimura, Goro}, + title = {On the field of rationality for an abelian variety}, + journal = {Nagoya Math. J.}, + year = {1972}, + volume = {45}, + pages = {167--178}, + fjournal = {Nagoya Mathematical Journal}, + issn = {0027-7630}, + mrclass = {14K15 (14G05 14K10)}, + mrnumber = {MR0306215 (46 \#5342)}, + mrreviewer = {M. J. Greenberg} +} + +@misc{sikora-2001, + author = {Adam S. Sikora}, + title = {Analogies between group actions on 3-manifolds and number fields}, + year = {2001}, + url = {http://www.citebase.org/abstract?id=oai:arXiv.org:math/0107210}, + +} + +@article{Silverman92, + author = {Silverman, Joseph H.}, + title = {Some arithmetic properties of {W}eierstrass points: + hyperelliptic curves}, + journal = {Bol. Soc. Brasil. Mat. (N.S.)}, + year = {1990}, + volume = {21}, + number = {1}, + pages = {11--50}, + fjournal = {Boletim da Sociedade Brasileira de Matem\'atica. Nova S\'erie}, + issn = {0100-3569}, + mrclass = {11G35 (14H25 14H55)}, + mrnumber = {MR1139554 (92k:11066)}, + mrreviewer = {Philippe Satg{\'e}} +} + + +@article{Torres94, + author = {Torres, Fernando}, + title = {Weierstrass points and double coverings of curves. {W}ith + application: symmetric numerical semigroups which cannot be + realized as {W}eierstrass semigroups}, + journal = {Manuscripta Math.}, + year = {1994}, + volume = {83}, + number = {1}, + pages = {39--58}, + coden = {MSMHB2}, + fjournal = {Manuscripta Mathematica}, + issn = {0025-2611}, + mrclass = {14H55 (30F20)}, + mrnumber = {MR1265917 (95a:14033)}, + mrreviewer = {R. F. Lax} +} + +@article{Towse96, + author = {Towse, Christopher}, + title = {Weierstrass points on cyclic covers of the projective line}, + journal = {Trans. Amer. Math. Soc.}, + year = {1996}, + volume = {348}, + number = {8}, + pages = {3355--3378}, + coden = {TAMTAM}, + fjournal = {Transactions of the American Mathematical Society}, + issn = {0002-9947}, + mrclass = {14H55 (11G30 14H45)}, + mrnumber = {MR1357406 (96k:14024)}, + mrreviewer = {Masaaki Homma} +} + +@article{Towse98, + author = {Towse, Christopher}, + title = {Weierstrass weights of fixed points of an involution}, + journal = {Math. Proc. Cambridge Philos. Soc.}, + year = {1997}, + volume = {122}, + number = {3}, + pages = {385--392}, + coden = {MPCPCO}, + fjournal = {Mathematical Proceedings of the Cambridge Philosophical + Society}, + issn = {0305-0041}, + mrclass = {14H55 (14E09 30F30)}, + mrnumber = {MR1466643 (98i:14033)}, + mrreviewer = {Masaaki Homma} +} + +@article{Weil56, + author = {Weil, Andr{\'e}}, + title = {The field of definition of a variety}, + journal = {Amer. J. Math.}, + year = {1956}, + volume = {78}, + pages = {509--524}, + fjournal = {American Journal of Mathematics}, + issn = {0002-9327}, + mrclass = {14.0X}, + mrnumber = {MR0082726 (18,601a)}, + mrreviewer = {P. Samuel} +} + +@article{accola70, + author = {Accola, Robert D. M.}, + title = {Two theorems on {R}iemann surfaces with noncyclic automorphism + groups.}, + journal = {Proc. Amer. Math. Soc.}, + year = {1970}, + volume = {25}, + pages = {598--602}, + fjournal = {Proceedings of the American Mathematical Society}, + issn = {0002-9939}, + mrclass = {30.45}, + mrnumber = {MR0259105 (41 \#3747)}, + mrreviewer = {N. L. Alling} +} + +@article{Brauer51, + author = {Brauer, Richard}, + title = {Beziehungen zwischen {K}lassenzahlen von {T}eilk\"orpern eines + galoisschen {K}\"orpers}, + journal = {Math. Nachr.}, + year = {1951}, + volume = {4}, + pages = {158--174}, + fjournal = {Mathematische Nachrichten}, + issn = {0025-584X}, + mrclass = {10.0X}, + mrnumber = {MR0039760 (12,593b)}, + mrreviewer = {T. Nakayama} +} + +@article{GeerSchoof, + author = {van der Geer, Gerard and Schoof, Ren{\'e}}, + title = {Effectivity of {A}rakelov divisors and the theta divisor of a number field}, + journal = {Selecta Math. (N.S.)}, + year = 2000, + volume = {6}, + number = 4, + pages = {377--398}, + month = {June}, + file = {/home/kontogar/Papers/pdf/geer-selecta.pdf}, + coden = {SMATF6}, + fjournal = {Selecta Mathematica. New Series}, + issn = {1022-1824}, + mrclass = {11R42 (11G30 14G25)}, + mrnumber = {MR1847381 (2002e:11157)}, + mrreviewer = {Pascal Autissier} +} + +@book{Janusz, + author = {Janusz, Gerald J.}, + title = {Algebraic number fields}, + year = {1996}, + volume = {7}, + series = {Graduate Studies in Mathematics}, + address = {Providence, RI}, + edition = {Second}, + isbn = {0-8218-0429-4}, + mrclass = {11Rxx (11-02 11R37)}, + mrnumber = {MR1362545 (96j:11137)}, + mrreviewer = {W. Narkiewicz}, + pages = {x+276}, + publisher = {American Mathematical Society} +} + +@article {Kani:86, + AUTHOR = {Kani, Ernst}, + TITLE = {The {G}alois-module structure of the space of holomorphic + differentials of a curve}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {367}, + YEAR = {1986}, + PAGES = {187--206}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {14H05 (14F10 14H30)}, + MRNUMBER = {839131 (88f:14024)}, +MRREVIEWER = {Shoichi Nakajima}, + DOI = {10.1515/crll.1986.367.187}, + URL = {http://dx.doi.org/10.1515/crll.1986.367.187}, +} + + +@article{Kani85, + author = {Kani, Ernst}, + title = {Relations between the genera and between the {H}asse-{W}itt + invariants of {G}alois coverings of curves}, + journal = {Canad. Math. Bull.}, + year = {1985}, + volume = {28}, + number = {3}, + pages = {321--327}, + coden = {CMBUA3}, + fjournal = {Canadian Mathematical Bulletin. Bulletin Canadien de + Math\'ematiques}, + issn = {0008-4395}, + mrclass = {14H30 (14H25)}, + mrnumber = {MR790953 (87b:14013)}, + mrreviewer = {T. Ono} +} + +@article{KaniRosen89, + author = {Kani, E. and Rosen, M.}, + title = {Idempotent relations and factors of {J}acobians}, + journal = {Math. Ann.}, + year = {1989}, + volume = {284}, + number = {2}, + pages = {307--327}, + coden = {MAANA}, + fjournal = {Mathematische Annalen}, + issn = {0025-5831}, + mrclass = {14K05 (14H35)}, + mrnumber = {MR1000113 (90h:14057)}, + mrreviewer = {H.-G. R{\"u}ck} +} + +@article{KaniRosen94, + author = {Kani, Ernst and Rosen, Michael}, + title = {Idempotent relations among arithmetic invariants attached to + number fields and algebraic varieties}, + journal = {J. Number Theory}, + year = {1994}, + volume = {46}, + number = {2}, + pages = {230--254}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X}, + mrclass = {11G40 (11R23 14G10 14J20)}, + mrnumber = {MR1269254 (95c:11080)}, + mrreviewer = {Am{\'{\i}}lcar Pacheco} +} + +@book{Neu, + author = {Neukirch, J\"urgen}, + title = {Algebraische {Z}ahlentheorie.}, + year = {1992}, + language = {German}, + publisher = {Springer-Verlag Berlin} +} + +@book{NeuEn, + author = {Neukirch, J{\"u}rgen}, + title = {Algebraic {N}umber {T}heory}, + year = {1999}, + volume = {322}, + series = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + address = {Berlin}, + note = {Translated from the 1992 German original and with a note by + Norbert Schappacher, + With a foreword by G. Harder}, + isbn = {3-540-65399-6}, + mrclass = {11Rxx (11-02 11S15 11S31 14C40)}, + mrnumber = {MR1697859 (2000m:11104)}, + mrreviewer = {Cornelius Greither}, + pages = {xviii+571}, + publisher = {Springer-Verlag} +} + +@article{Abramovich, + author = {Abramovich, Dan}, + title = {A linear lower bound on the gonality of modular curves}, + journal = {Internat. Math. Res. Notices}, + year = {1996}, + number = {20}, + pages = {1005--1011}, + fjournal = {International Mathematics Research Notices}, + issn = {1073-7928}, + mrclass = {11G18 (11F32 14G35)}, + mrnumber = {MR1422373 (98b:11063)}, + mrreviewer = {M. Ram Murty} +} + +@article{Bro-Stev, + author = {Br\"oker, Reinier and Stevenhagen, Peter}, + title = {{Constructing Elliptic Curves of Prime Order }}, + journal = {Preprint}, + year = 2007, + file = {/media/KINGSTON/Papers/pdf/primeorderStevenBroker.pdf}, + +} + +@article {garciaa-s, + AUTHOR = {Garc{\'{\i}}a, Arnaldo}, + TITLE = {On {W}eierstrass points on {A}rtin-{S}chreier extensions of + {$k(x)$}}, + JOURNAL = {Math. Nachr.}, + FJOURNAL = {Mathematische Nachrichten}, + VOLUME = {144}, + YEAR = {1989}, + PAGES = {233--239}, + ISSN = {0025-584X}, + CODEN = {MTMNAQ}, + MRCLASS = {14H05 (14H55)}, + MRNUMBER = {MR1037171 (91f:14021)}, +MRREVIEWER = {K. Kiyek}, + DOI = {10.1002/mana.19891440116}, + URL = {http://dx.doi.org/10.1002/mana.19891440116}, +} + + + + +@book{Farkas-Kra, + author = {Farkas, Hershel M. and Kra, Irwin}, + title = {Riemann surfaces}, + year = 1980, + volume = {71}, + series = {Graduate Texts in Mathematics}, + address = {New York}, + isbn = {0-387-90465-4}, + mrclass = {30Fxx (14-01)}, + mrnumber = {MR583745 (82c:30067)}, + mrreviewer = {M. Herv{\'e}}, + pages = {xi+337}, + publisher = {Springer-Verlag} +} + +@article{Elkies90, + author = {Elkies, Noam D.}, + title = {The automorphism group of the modular curve {$X\sb 0(63)$}}, + journal = {Compositio Math.}, + year = {1990}, + volume = {74}, + number = {2}, + pages = {203--208}, + coden = {CMPMAF}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {11G18 (11F03 14G25)}, + mrnumber = {MR1047740 (91e:11064)}, + mrreviewer = {Sheldon Kamienny} +} + +@article{Hasegawa-Shimura, + author = {Hasegawa, Yuji and Shimura, Mahoro}, + title = {Trigonal modular curves {$X\sp {+d}\sb 0(N)$}}, + journal = {Proc. Japan Acad. Ser. A Math. Sci.}, + year = {1999}, + volume = {75}, + number = {9}, + pages = {172--175}, + coden = {PJAADT}, + fjournal = {Japan Academy. Proceedings. Series A. Mathematical Sciences}, + issn = {0386-2194}, + mrclass = {11G18 (11G30)}, + mrnumber = {MR1740817 (2001d:11063)}, + mrreviewer = {Chandrashekhar Khare} +} + +@article {KonstKonto1, + AUTHOR = {Konstantinou, Elisavet and Kontogeorgis, Aristides}, + TITLE = {Computing polynomials of the {R}amanujan {$t_n$} class + invariants}, + JOURNAL = {Canad. Math. Bull.}, + FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de + Math\'ematiques}, + VOLUME = {52}, + YEAR = {2009}, + NUMBER = {4}, + PAGES = {583--597}, + ISSN = {0008-4395}, + CODEN = {CMBUA3}, + MRCLASS = {11R29 (11F20 11G15 11R20 11R37)}, + MRNUMBER = {2567152 (2011a:11200)}, +MRREVIEWER = {Daniel C. Mayer}, + DOI = {10.4153/CMB-2009-058-6}, + URL = {http://dx.doi.org/10.4153/CMB-2009-058-6}, +} + +@article {KonstKonto2, + AUTHOR = {Konstantinou, Elisavet and Kontogeorgis, Aristides}, + TITLE = {Ramanujan's class invariants and their use in elliptic curve + cryptography}, + JOURNAL = {Comput. Math. Appl.}, + FJOURNAL = {Computers \& Mathematics with Applications. An International + Journal}, + VOLUME = {59}, + YEAR = {2010}, + NUMBER = {8}, + PAGES = {2901--2917}, + ISSN = {0898-1221}, + CODEN = {CMAPDK}, + MRCLASS = {94A60 (11T71 14G50)}, + MRNUMBER = {2607997 (2010m:94101)}, + DOI = {10.1016/j.camwa.2010.02.008}, + URL = {http://dx.doi.org/10.1016/j.camwa.2010.02.008}, +} + + + +@article{Kenku-Momose, + author = {Kenku, M. A. and Momose, Fumiyuki}, + title = {Automorphism groups of the modular curves {$X\sb 0(N)$}}, + journal = {Compositio Math.}, + year = {1988}, + volume = {65}, + number = {1}, + pages = {51--80}, + coden = {CMPMAF}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {14G25 (11G30 14K15)}, + mrnumber = {MR930147 (88m:14015)}, + mrreviewer = {Kenneth A. Ribet} +} + +@article{Kim-Sarnak, + author = {Kim, Henry H.}, + title = {Functoriality for the exterior square of {${\rm GL}\sb 4$} and + the symmetric fourth of {${\rm GL}\sb 2$}}, + journal = {J. Amer. Math. Soc.}, + year = {2003}, + volume = {16}, + number = {1}, + pages = {139--183 (electronic)}, + note = {With appendix 1 by Dinakar Ramakrishnan and appendix 2 by Kim + and Peter Sarnak}, + fjournal = {Journal of the American Mathematical Society}, + issn = {0894-0347}, + mrclass = {11F70 (11R39 22E46)}, + mrnumber = {MR1937203 (2003k:11083)}, + mrreviewer = {Mahdi Asgari} +} + +@article{KoPhd, + author = {Kontogeorgis, Aristides}, + title = {On Automorphisms of certain algebraic curves and varieties}, + journal = {Ph.D. dissertation University of Crete (In Greek)}, + year = {1999}, + +} + +@article{MazurAlex, + author = {Mazur, Barry}, + title = {Remarks on the {A}lexander Polynomial}, + journal = {Unpublished Article}, + year = {1964}, +} + + + +@article{MezardPhd, + author = {M\'ezard, Ariane}, + title = { +Quelques probl\`emes de d\'eformations en caract\'eristique mixte +}, + journal = {Ph.D. dissertation, Universit\'e Joseph Fourier Grenoble}, + year = {1998}, + +} + +@article{Li-Yau, + author = {Li, Peter and Yau, Shing Tung}, + title = {A new conformal invariant and its applications to the {W}illmore conjecture and the first eigenvalue of compact surfaces}, + journal = {Invent. Math.}, + year = 1982, + volume = {69}, + number = 2, + pages = {269--291}, + file = {/home/kontogar/Papers/pdf/LiYau.pdf}, + coden = {INVMBH}, + fjournal = {Inventiones Mathematicae}, + issn = {0020-9910}, + mrclass = {53C40 (53C21 58G25)}, + mrnumber = {MR674407 (84f:53049)}, + mrreviewer = {Yu. Burago} +} + +@article{LRS, + author = {Luo, W. and Rudnick, Z. and Sarnak, P.}, + title = {On {S}elberg's eigenvalue conjecture}, + journal = {Geom. Funct. Anal.}, + year = {1995}, + volume = {5}, + number = {2}, + pages = {387--401}, + coden = {GFANFB}, + fjournal = {Geometric and Functional Analysis}, + issn = {1016-443X}, + mrclass = {11F72 (11F70)}, + mrnumber = {MR1334872 (96h:11045)}, + mrreviewer = {Jens Bolte} +} + +@article{Poonen-gonality, + AUTHOR = {Poonen, Bjorn}, + TITLE = {Gonality of modular curves in characteristic {$p$}}, + JOURNAL = {Math. Res. Lett.}, + FJOURNAL = {Mathematical Research Letters}, + VOLUME = {14}, + YEAR = {2007}, + NUMBER = {4}, + PAGES = {691--701}, + ISSN = {1073-2780}, + MRCLASS = {11G18 (14G35 14H51)}, + MRNUMBER = {2335995}, +MRREVIEWER = {Am\'{\i}lcar Pacheco}, + DOI = {10.4310/MRL.2007.v14.n4.a14}, + URL = {https://doi.org/10.4310/MRL.2007.v14.n4.a14} +} + + + +@article {Rajan98, + + AUTHOR = {Rajan, C. S.}, + + TITLE = {Automorphisms of {$X(11)$} over characteristic {$3$} and the + + {M}athieu group {$M\sb {11}$}}, + + JOURNAL = {J. Ramanujan Math. Soc.}, + + FJOURNAL = {Journal of the Ramanujan Mathematical Society}, + + VOLUME = {13}, + + YEAR = {1998}, + + NUMBER = {1}, + + PAGES = {63--72}, + + ISSN = {0970-1249}, + + MRCLASS = {14G35 (11G18 14E09 14H45 20D08)}, + + MRNUMBER = {MR1626720 (99f:14027)}, + +MRREVIEWER = {Akio Tamagawa}, + +} + + + +@article {Rankin, + + AUTHOR = {Rankin, R. A.}, + + TITLE = {The construction of automorphic forms from the derivatives of + + a given form}, + + JOURNAL = {J. Indian Math. Soc. (N.S.)}, + + VOLUME = {20}, + + YEAR = {1956}, + + PAGES = {103--116}, + + MRCLASS = {33.0X}, + + MRNUMBER = {MR0082563 (18,571c)}, + +MRREVIEWER = {E. Grosswald}, + +} + + + +@article {Ritzenthaler03, + + AUTHOR = {Ritzenthaler, Christophe}, + + TITLE = {Automorphismes des courbes modulaires {$X(n)$} en + + caract\'eristique {$p$}}, + + JOURNAL = {Manuscripta Math.}, + + FJOURNAL = {Manuscripta Mathematica}, + + VOLUME = {109}, + + YEAR = {2002}, + + NUMBER = {1}, + + PAGES = {49--62}, + + ISSN = {0025-2611}, + + CODEN = {MSMHB2}, + + MRCLASS = {11G18}, + + MRNUMBER = {MR1931207 (2003g:11067)}, + +MRREVIEWER = {Andrea Mori}, + +} +@book {GriffithsRS, + AUTHOR = {Griffiths, Phillip A.}, + TITLE = {Introduction to algebraic curves}, + SERIES = {Translations of Mathematical Monographs}, + VOLUME = {76}, + NOTE = {Translated from the Chinese by Kuniko Weltin}, + PUBLISHER = {American Mathematical Society}, + ADDRESS = {Providence, RI}, + YEAR = {1989}, + PAGES = {x+221}, + ISBN = {0-8218-4530-6}, + MRCLASS = {14Hxx (14-01 14H10 30F10)}, + MRNUMBER = {1013999 (90i:14028)}, +MRREVIEWER = {Werner Kleinert}, +} + + + +@incollection{Selberg65, + author = {Selberg, Atle}, + title = {On the estimation of {F}ourier coefficients of modular forms}, + booktitle = {Proc. Sympos. Pure Math., Vol. VIII}, + pages = {1--15}, + publisher = {Amer. Math. Soc.}, + year = {1965}, + address = {Providence, R.I.}, + mrclass = {10.20}, + mrnumber = {MR0182610 (32 \#93)}, + mrreviewer = {J. R. Smart} +} + +@article{SarnakNOTICES, + author = {Sarnak, Peter}, + title = {Selberg's eigenvalue conjecture}, + journal = {Notices Amer. Math. Soc.}, + year = {1995}, + volume = {42}, + number = {11}, + pages = {1272--1277}, + coden = {AMNOAN}, + fjournal = {Notices of the American Mathematical Society}, + issn = {0002-9920}, + mrclass = {11F72}, + mrnumber = {MR1355461 (97c:11059)}, + mrreviewer = {Joachim Schwermer} +} + +@incollection{SerreXp, + author = {Serre, Jean-Pierre}, + title = {Appendix to {B}. {M}azur, {O}pen problems regarding rational points on curves and + varieties}, + booktitle = {Galois representations in arithmetic algebraic geometry + (Durham, 1996)}, + pages = {239--265}, + publisher = {Cambridge Univ. Press}, + year = {1998}, + volume = {254}, + series = {London Math. Soc. Lecture Note Ser.}, + address = {Cambridge}, + mrclass = {14G05 (11G35 14G25)}, + mrnumber = {MR1696485 (2000g:14031)}, + mrreviewer = {Dan Abramovich} +} + +@book{ShimuraBook, + author = {Shimura, Goro}, + title = {Introduction to the arithmetic theory of automorphic + functions}, + year = {1994}, + volume = {11}, + series = {Publications of the Mathematical Society of Japan}, + address = {Princeton, NJ}, + note = {Reprint of the 1971 original, + Kano Memorial Lectures, 1}, + isbn = {0-691-08092-5}, + mrclass = {11Fxx (11-02 11G05 11G40)}, + mrnumber = {MR1291394 (95e:11048)}, + pages = {xiv+271}, + publisher = {Princeton University Press} +} + +@article{siegel45, + author = {Siegel Carl Ludwig}, + title = {Some Remarks on Discontinuous Groups}, + journal = {The Annals of Mathematics 2nd Ser.}, + year = {1945}, + volume = {46 No. 4}, + pages = {108--118}, + +} + +@article{Yang-Yau, + author = {Yang, Paul C. and Yau, Shing Tung}, + title = {Eigenvalues of the {L}aplacian of compact {R}iemann surfaces + and minimal submanifolds}, + journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)}, + year = {1980}, + volume = {7}, + number = {1}, + pages = {55--63}, + coden = {PSNAAI}, + fjournal = {Annali della Scuola Normale Superiore di Pisa. Classe di + Scienze. Serie IV}, + mrclass = {58G25 (49G10 53C20)}, + mrnumber = {MR577325 (81m:58084)}, + mrreviewer = {Scott Wolpert} +} + +@article{EGAIII1, + author = {Grothendieck, A.}, + title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {III}. \'{E}tude + cohomologique des faisceaux coh\'erents. {I}}, + journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, + year = {1961}, + number = {11}, + pages = {167}, + fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications + Math\'ematiques}, + issn = {0073-8301}, + mrclass = {14.55}, + mrnumber = {MR0217085 (36 \#177c)} +} + +@incollection{Elkies99, + author = {Elkies, Noam D.}, + title = {Linearized algebra and finite groups of {L}ie type. {I}. + {L}inear and symplectic groups}, + booktitle = {Applications of curves over finite fields (Seattle, WA, 1997)}, + pages = {77--107}, + publisher = {Amer. Math. Soc.}, + year = {1999}, + volume = {245}, + series = {Contemp. Math.}, + address = {Providence, RI}, + mrclass = {20G40 (11G25 12F12 13A50)}, + mrnumber = {MR1732230 (2001a:20082)}, + mrreviewer = {R. W. Carter} +} + +@article {CaldRam, + AUTHOR = {Maldonado-Ram{\'{\i}}rez, Myriam Rosal{\'{\i}}a and + Rzedowski-Calder{\'o}n, Martha}, + TITLE = {Cyclic {$p$}-extensions of function fields with null + {H}asse-{W}itt map}, + JOURNAL = {Int. Math. Forum}, + FJOURNAL = {International Mathematical Forum. Journal for Theory and + Applications}, + VOLUME = {2}, + YEAR = {2007}, + NUMBER = {49-52}, + PAGES = {2463--2480}, + ISSN = {1312-7594}, + MRCLASS = {11R58 (14H05)}, + MRNUMBER = {MR2381834}, +} + + + +@book{Goldschmidt, + author = {Goldschmidt, David M.}, + title = {Algebraic functions and projective curves}, + year = {2003}, + volume = {215}, + series = {Graduate Texts in Mathematics}, + address = {New York}, + isbn = {0-387-95432-5}, + mrclass = {14-01 (14Hxx)}, + mrnumber = {MR1934359 (2003j:14001)}, + mrreviewer = {C{\'{\i}}cero Fernandes de Carvalho}, + pages = {xvi+179}, + publisher = {Springer-Verlag} +} + +@book{GossBook, + author = {Goss, David}, + title = {Basic structures of function field arithmetic}, + year = {1996}, + volume = {35}, + series = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results + in Mathematics and Related Areas (3)]}, + address = {Berlin}, + isbn = {3-540-61087-1}, + mrclass = {11G09 (11L05 11R58)}, + mrnumber = {MR1423131 (97i:11062)}, + mrreviewer = {Jeremy T. Teitelbaum}, + pages = {xiv+422}, + publisher = {Springer-Verlag} +} + +@article{Harbater:80, + author = {Harbater, David}, + title = {Moduli of {$p$}-covers of curves}, + journal = {Comm. Algebra}, + year = {1980}, + volume = {8}, + number = {12}, + pages = {1095--1122}, + coden = {COALDM}, + fjournal = {Communications in Algebra}, + issn = {0092-7872}, + mrclass = {14D15 (14H30)}, + mrnumber = {MR579791 (82f:14010)}, + mrreviewer = {David Cox} +} + +@article{Koeck:04, + author = {K{\"o}ck, Bernhard}, + title = {Galois structure of {Z}ariski cohomology for weakly ramified covers of curves}, + journal = {Amer. J. Math.}, + year = 2004, + volume = {126}, + number = 5, + pages = {1085--1107}, + file = {/media/KINGSTON/Papers/pdf/kockAJM}, + coden = {AJMAAN}, + fjournal = {American Journal of Mathematics}, + issn = {0002-9327}, + mrclass = {11R33 (11G30 14H30)}, + mrnumber = {MR2089083 (2005i:11163)}, + mrreviewer = {Nigel Byott} +} + +@article{CL-MM, + author = {Lehr, Claus and Matignon, Michel}, + title = {Automorphism groups for {$p$}-cyclic covers of the affine + line}, + journal = {Compos. Math.}, + year = {2005}, + volume = {141}, + number = {5}, + pages = {1213--1237}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {14H37 (14H30)}, + mrnumber = {MR2157136 (2006f:14029)}, + mrreviewer = {Am{\'{\i}}lcar Pacheco} +} + +@article{MMat, + author = {Matignon, Michel}, + title = {Email communication, 26 August 2006}, + journal = {}, + year= {2006} + +} + +@article{Magma1997, + author = {Bosma, Wieb and Cannon, John and Playoust, Catherine}, + title = {The {M}agma algebra system {I}: {T}he user language}, + journal = {J. Symbolic Comput.}, + year = 1997, + volume = 24, + number = {3-4}, + pages = {235-265}, + note = {Computational algebra and number theory (London, 1993)}, + url = {http://www.maths.usyd.edu.au:8000/u/magma/}, + fjournal = {Journal of Symbolic Computation}, + issn = {0747-7171} +} + + + + +@article{CoKool, +author = {Cornlissen, Gunther and Kool, Janne}, +title = {Measure-theoretic rigidity for {M}umford curves}, +journal = {Ergodic Theory and Dynamical Systems}, +volume = {33}, +issue = {03}, +month = {6}, +year = {2013}, +issn = {1469-4417}, +pages = {851--869}, +numpages = {19}, +doi = {10.1017/S0143385712000016}, +URL = {http://journals.cambridge.org/article_S0143385712000016}, +} + + +@article{IJNTKOKO, + author = {Konstantinou, Elisavet and Kontogeorgis, Aristides}, + title = {Ramanujan Invariants for discriminants congruent to 5 mod 24}, + journal = {arXiv:math.NT, to appear in International Journal of Number Theory}, + year = {2011}, + number = {arXiv:1107.0413} +} +@incollection {MR1846457, + AUTHOR = {Stevenhagen, Peter}, + TITLE = {Hilbert's 12th problem, complex multiplication and {S}himura + reciprocity}, + BOOKTITLE = {Class field theory---its centenary and prospect ({T}okyo, + 1998)}, + SERIES = {Adv. Stud. Pure Math.}, + VOLUME = {30}, + PAGES = {161--176}, + PUBLISHER = {Math. Soc. Japan}, + ADDRESS = {Tokyo}, + YEAR = {2001}, + MRCLASS = {11R37 (11G15)}, + MRNUMBER = {1846457 (2002i:11110)}, +MRREVIEWER = {Xianke Zhang}, +} + + +@book {RamNotebooks, + AUTHOR = {Ramanujan, Srinivasa}, + TITLE = {Notebooks. {V}ols. 1, 2}, + PUBLISHER = {Tata Institute of Fundamental Research}, + ADDRESS = {Bombay}, + YEAR = {1957}, + PAGES = {Vol. 1. vi+351 pp.; Vol. 2. vi+393}, + MRCLASS = {01.00 (10.00)}, + MRNUMBER = {0099904 (20 \#6340)}, +MRREVIEWER = {S. Chowla}, +} + + + + +@article {Berndt-Chan, + AUTHOR = {Berndt, Bruce C. and Chan, Heng Huat}, + TITLE = {Ramanujan and the modular {$j$}-invariant}, + JOURNAL = {Canad. Math. Bull.}, + FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de + Math\'ematiques}, + VOLUME = {42}, + YEAR = {1999}, + NUMBER = {4}, + PAGES = {427--440}, + ISSN = {0008-4395}, + CODEN = {CMBUA3}, + MRCLASS = {11F03 (11R37 33C05 33E05)}, + MRNUMBER = {1727340 (2002a:11035)}, + DOI = {10.4153/CMB-1999-050-1}, + URL = {http://dx.doi.org/10.4153/CMB-1999-050-1}, +} + +@incollection {GeeStevenhagen, + AUTHOR = {Gee, Alice and Stevenhagen, Peter}, + TITLE = {Generating class fields using {S}himura reciprocity}, + BOOKTITLE = {Algorithmic number theory ({P}ortland, {OR}, 1998)}, + SERIES = {Lecture Notes in Comput. Sci.}, + VOLUME = {1423}, + PAGES = {441--453}, + PUBLISHER = {Springer}, + ADDRESS = {Berlin}, + YEAR = {1998}, + MRCLASS = {11R37 (11F03 11G15)}, + MRNUMBER = {1726092 (2000m:11112)}, +MRREVIEWER = {Xianke Zhang}, + DOI = {10.1007/BFb0054883}, + URL = {http://dx.doi.org/10.1007/BFb0054883}, +} + +@article {GeeBordeaux, + AUTHOR = {Gee, Alice}, + TITLE = {Class invariants by {S}himura's reciprocity law}, + NOTE = {Les XX{\`e}mes Journ{\'e}es Arithm{\'e}tiques (Limoges, 1997)}, + JOURNAL = {J. Th\'eor. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux}, + VOLUME = {11}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {45--72}, + ISSN = {1246-7405}, + MRCLASS = {11R37 (11F11 11G15)}, + MRNUMBER = {1730432 (2000i:11171)}, +MRREVIEWER = {Cornelius Greither}, + URL = {http://jtnb.cedram.org/item?id=JTNB_1999__11_1_45_0}, +} + + + + +@article{CKa, + author = {Gunther Cornelissen and Fumiharu Kato}, + title = {{Equivariant deformation of Mumford curves and of ordinary + curves in positive characteristic}}, + journal = {arXiv:math.AG/0103207, to appear in Duke Math. J.}, + +} + +@phdthesis{Jor:81, + author = {Jordan, B. W.}, + title = {On the diophantine arithmetic of Shimura Curves}, + school = {Harvard}, + year = {1981}, + +} + +@phdthesis{Ko:phd, + author = {Kontogeorgis, Aristides}, + title = {On the group of automorphisms of certain algebraic curves}, + school = {University of Crete}, + year = {1999}, + note = {(In Greek)}, + +} + +@article{KoArxiv, +author = {Kontogeorgis, Aristides}, +title = {Deformations of Curves with Automorphisms and representations +on Riemann-Roch spaces}, +journal = {arXiv:0804.1647v1}, +} +@article{GiuKo, +author = {Massimo Giulietti and Gabor Korchmaros}, +title = {On large automorphism groups of algebraic curves in positive characteristic}, +journal = {arXiv:0706.2320v1 }, +} + + +@article{Ogg:77, + author = {Ogg, A. P.}, + title = {\"{U}ber die {A}utomorphismengruppe von {$X\sb{0}(N)$}}, + journal = {Math. Ann.}, + year = {1977}, + volume = {228}, + number = {3}, + pages = {279--292}, + mrclass = {10D05 (14G25 14H25 14K15)}, + mrnumber = {58 \#27775} +} + +@incollection{Ogg:85, + author = {Ogg, A. P.}, + title = {Real points on {S}himura curves}, + booktitle = {Arithmetic and geometry, Vol. I}, + pages = {277--307}, + publisher = {Birkh\"auser Boston}, + year = {1983}, + volume = {35}, + series = {Progr. Math.}, + address = {Boston, MA}, + mrclass = {11G18 (11G15 11R52 14G20)}, + mrnumber = {85m:11034}, + mrreviewer = {Yasutaka Ihara} +} +@article {Ihara, + AUTHOR = {Ihara, Yasutaka}, + TITLE = {Some remarks on the number of rational points of algebraic + curves over finite fields}, + JOURNAL = {J. Fac. Sci. Univ. Tokyo Sect. IA Math.}, + FJOURNAL = {Journal of the Faculty of Science. University of Tokyo. + Section IA. Mathematics}, + VOLUME = {28}, + YEAR = {1981}, + NUMBER = {3}, + PAGES = {721--724 (1982)}, + ISSN = {0040-8980}, + CODEN = {JFTMAT}, + MRCLASS = {14G15 (14G13 14H25 94B05)}, + MRNUMBER = {MR656048 (84c:14016)}, +MRREVIEWER = {M. A. Kenku}, +} +@article{Rev:97, + author = {Reversat, Marc}, + title = {Sur les rev\^etements de {S}chottky des courbes modulaires de + {D}rinfeld}, + journal = {Arch. Math. (Basel)}, + year = {1996}, + volume = {66}, + number = {5}, + pages = {378--387}, + coden = {ACVMAL}, + fjournal = {Archiv der Mathematik. Archives of Mathematics. Archives + Math\'ematiques}, + issn = {0003-889X}, + mrclass = {11G20 (14H30)}, + mrnumber = {97e:11073}, + mrreviewer = {Ernst-Ulrich Gekeler} +} + +@article{Rod:2002, + author = {Rotger, Victor}, + title = {On the group of automorphisms of {S}himura curves and + applications}, + journal = {Compositio Math.}, + year = {2002}, + volume = {132}, + number = {2}, + pages = {229--241}, + coden = {CMPMAF}, + fjournal = {Compositio Mathematica}, + issn = {0010-437X}, + mrclass = {11G18 (14G35)}, + mrnumber = {2003c:11065}, + mrreviewer = {Hui Xue} +} + +@article{Serre:96, + author = {Serre, Jean-Pierre}, + title = {The automorphism group of ${X}(p)$}, + journal = {London Math Soc. Lencture Notes Series}, + year = {1998}, + volume = {254}, + note = {(copied from a letter dated June 26, 1996), + appendix to B. Mazur, Open problems regarding rational points + on curves and varieties in: Galois representations + in arithmetic algebraic geometry (A.J.Scholl and R.L. Taylor, eds.)}, + +} + +@phdthesis{bornephd, + author = {Borne, Niels}, + title = {Une formule de Riemann-Roch \'equivariante pour les courbes}, + school = {Laboratoire de Math\'ematiques Pures de l\`{} Universit\'e Bordeaux}, + year = 2000, + file = {/home/kontogar/Papers/pdf/Thesepdf.pdf}, + +} + +@article{borne04, + author = {Borne, Niels}, + title = {A relative {S}hafarevich theorem}, + journal = {Math. Z.}, + year = 2004, + volume = {248}, + number = 2, + pages = {351--367}, + file = {/home/kontogar/Papers/pdf/Shaf3.pdf}, + coden = {MAZEAX}, + fjournal = {Mathematische Zeitschrift}, + issn = {0025-5874}, + mrclass = {14H30 (20C20)}, + mrnumber = {MR2088933 (2005g:14058)}, + mrreviewer = {Am{\'{\i}}lcar Pacheco} +} + +@article{borne06, + author = {Borne, Niels}, + title = {Cohomology of {$G$}-sheaves in positive characteristic}, + journal = {Adv. Math.}, + year = {2006}, + volume = {201}, + number = {2}, + pages = {454--515}, + coden = {ADMTA4}, + fjournal = {Advances in Mathematics}, + issn = {0001-8708}, + mrclass = {14C35 (11R33 19Dxx)}, + mrnumber = {MR2211535} +} + +@article{Deuring, + author = {Deuring, Max}, + title = {Automorphismen und {D}ivisorenklassen der {O}rdnung {$\iota$} + in algebraischen {F}unktionenk\"orpern}, + journal = {Math. Ann.}, + year = {1937}, + volume = {113}, + number = {1}, + pages = {208--215}, + coden = {MAANA}, + fjournal = {Mathematische Annalen}, + issn = {0025-5831}, + mrclass = {Contributed Item}, + mrnumber = {MR1513087} +} + + + +@article {AKRo1, + AUTHOR = {Kontogeorgis, Aristides and Rotger, Victor}, + TITLE = {On the non-existence of exceptional automorphisms on {S}himura + curves}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {40}, + YEAR = {2008}, + NUMBER = {3}, + PAGES = {363--374}, + ISSN = {0024-6093}, + MRCLASS = {11G18 (14G35)}, + MRNUMBER = {2418792 (2009c:11089)}, +MRREVIEWER = {Marc-Hubert Nicole}, + DOI = {10.1112/blms/bdn012}, + URL = {http://dx.doi.org/10.1112/blms/bdn012}, +} +@article {AKRo2, + AUTHOR = {Kontogeorgis, Aristides and Rotger, Victor}, + TITLE = {On abelian automorphism groups of {M}umford curves}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {40}, + YEAR = {2008}, + NUMBER = {3}, + PAGES = {353--362}, + ISSN = {0024-6093}, + MRCLASS = {11G18 (14G20 14G35 14H37)}, + MRNUMBER = {2418791 (2009j:11098)}, +MRREVIEWER = {Patrick Erik Bradley}, + DOI = {10.1112/blms/bdn011}, + URL = {http://dx.doi.org/10.1112/blms/bdn011}, +} + + + +@article{Ko:2002a, + author = {Kontogeorgis, Aristides}, + title = {On the tangent space of the deformation functor of curves with automorphims}, + journal = {arXiv:math.AG/0201194 v4 2007}, + year = 2007, + +} + +@article{Madan77, + author = {Madan, Manohar L.}, + title = {On a theorem of {M}. {D}euring and {I}. {R}. \v {S}afarevi\v + c}, + journal = {Manuscripta Math.}, + year = {1977/78}, + volume = {23}, + number = {1}, + pages = {91--102}, + fjournal = {Manuscripta Mathematica}, + issn = {0025-2611}, + mrclass = {14H05 (12B20 12B10)}, + mrnumber = {MR0460335 (57 \#329)}, + mrreviewer = {Jose M. Aroca} +} + +@article{Nak:86, + author = {Nakajima, Sh{\=o}ichi}, + title = {Action of an automorphism of order {$p$} on cohomology groups + of an algebraic curve}, + journal = {J. Pure Appl. Algebra}, + year = {1986}, + volume = {42}, + number = {1}, + pages = {85--94}, + coden = {JPAAA2}, + fjournal = {Journal of Pure and Applied Algebra}, + issn = {0022-4049}, + mrclass = {14H30 (14E20)}, + mrnumber = {MR852320 (88d:14018)}, + mrreviewer = {K. Kiyek} +} + +@article{Nak:85, + author = {Nakajima, Sh{\=o}ichi}, + title = {Equivariant form of the {D}euring-\v {S}afarevi\v c formula + for {H}asse-{W}itt invariants}, + journal = {Math. Z.}, + year = {1985}, + volume = {190}, + number = {4}, + pages = {559--566}, + coden = {MAZEAX}, + fjournal = {Mathematische Zeitschrift}, + issn = {0025-5874}, + mrclass = {14H30 (14E20 14H40)}, + mrnumber = {87g:14024}, + mrreviewer = {Loren D. Olson} +} + +@article{Nak:87i, + author = {Nakajima, Sh{\=o}ichi}, + title = {Galois module structure of cohomology groups for tamely + ramified coverings of algebraic varieties}, + journal = {J. Number Theory}, + year = {1986}, + volume = {22}, + number = {1}, + pages = {115--123}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X}, + mrclass = {14E20 (11R34 14E40)}, + mrnumber = {87i:14010}, + mrreviewer = {Lindsay N. Childs} +} + +@article{Nak:85j, + author = {Nakajima, Sh{\=o}ichi}, + title = {On {G}alois module structure of the cohomology groups of an + algebraic variety}, + journal = {Invent. Math.}, + year = {1984}, + volume = {75}, + number = {1}, + pages = {1--8}, + coden = {INVMBH}, + fjournal = {Inventiones Mathematicae}, + issn = {0020-9910}, + mrclass = {14E20 (14F05)}, + mrnumber = {85j:14021}, + mrreviewer = {R. T. Hoobler} +} + +@article{Pries:05, + author = {Pries, Rachel J.}, + title = {Equiramified deformations of covers in positive characteristic}, + journal = {arXiv:math.AG/0403056 v3}, + year = 2005, + file = {/media/KINGSTON/Papers/pdf/RachelEquiramv3.pdf}, + +} + +@article{PriesNumTh, + author = {Pries, Rachel J.}, + title = {Wildly ramified covers with large genus}, + journal = {J. Number Theory}, + year = {2006}, + volume = {119}, + number = {2}, + pages = {194--209}, + coden = {JNUTA9}, + fjournal = {Journal of Number Theory}, + issn = {0022-314X}, + mrclass = {14H30 (14G32)}, + mrnumber = {MR2250044} +} + +@article{Schmid36, + author = {Schmid, Hermann Ludwig}, + title = {{Zur Arithmetik der zyklischen $p$-K\"orper.}}, + journal = {J. Reine Angew. Math.}, + year = {1936}, + volume = {176}, + pages = {161-167}, + keywords = {{Number fields, function fields}}, + language = {German} +} + +@article{Shaf47, + author = {Shafarevitch, I.}, + title = {On {$p$}-extensions}, + journal = {Rec. Math. [Mat. Sbornik] N.S., AMS Transl. series II}, + year = {1954}, + volume = {4}, + pages = {59-72}, + mrclass = {09.1X}, + mrnumber = {MR0020546 (8,560e)}, + mrreviewer = {G. Whaples} +} + +@article {SOS91, + AUTHOR = {Sekiguchi, T. and Oort, F. and Suwa, N.}, + TITLE = {On the deformation of {A}rtin-{S}chreier to {K}ummer}, + JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. + Quatri\`eme S\'erie}, + VOLUME = {22}, + YEAR = {1989}, + NUMBER = {3}, + PAGES = {345--375}, + ISSN = {0012-9593}, + CODEN = {ASENAH}, + MRCLASS = {14L15 (11G20)}, + MRNUMBER = {MR1011987 (91g:14041)}, +} + +@book {Walker, + AUTHOR = {Walker, Robert J.}, + TITLE = {Algebraic curves}, + PUBLISHER = {Dover Publications Inc.}, + ADDRESS = {New York}, + YEAR = {1962}, + PAGES = {x+201}, + MRCLASS = {14.00 (14.20)}, + MRNUMBER = {MR0144897 (26 \#2438)}, +} + +@book{SerreAlgGroupsClassFields, + author = {Serre, Jean-Pierre}, + title = {Algebraic groups and class fields}, + year = {1988}, + volume = {117}, + series = {Graduate Texts in Mathematics}, + address = {New York}, + note = {Translated from the French}, + isbn = {0-387-96648-X}, + mrclass = {14K30 (11G45 11S31 14L40)}, + mrnumber = {MR918564 (88i:14041)}, + pages = {x+207}, + publisher = {Springer-Verlag} +} + +@incollection{SerreMexico, + author = {Serre, Jean-Pierre}, + title = {Sur la topologie des vari\'et\'es alg\'ebriques en + caract\'eristique {$p$}}, + booktitle = {Symposium internacional de topolog\'\i a algebraica + International symposium on algebraic topology}, + pages = {24--53}, + publisher = {Universidad Nacional Aut\'onoma de M\'exico and UNESCO, Mexico + City}, + year = {1958}, + mrclass = {14.00}, + mrnumber = {MR0098097 (20 \#4559)}, + mrreviewer = {M. Rosenlicht} +} + +@book{SerreLinear, + author = {Serre, Jean-Pierre}, + title = {Linear representations of finite groups}, + year = {1977}, + address = {New York}, + note = {Translated from the second French edition by Leonard L. Scott, + Graduate Texts in Mathematics, Vol. 42}, + isbn = {0-387-90190-6}, + mrclass = {20CXX}, + mrnumber = {MR0450380 (56 \#8675)}, + mrreviewer = {W. Feit}, + pages = {x+170}, + publisher = {Springer-Verlag} +} + +@article{Stalder04, + author = {Stalder, Nicolas}, + title = {On {$p$}-rank representations}, + journal = {J. Algebra}, + year = {2004}, + volume = {280}, + number = {2}, + pages = {825--841}, + coden = {JALGA4}, + fjournal = {Journal of Algebra}, + issn = {0021-8693}, + mrclass = {14H37 (20C20)}, + mrnumber = {MR2090066 (2005h:14074)}, + mrreviewer = {Carlo Giovanni Madonna} +} + +@book{Berk:90, + author = {Berkovich, Vladimir G.}, + title = {Spectral theory and analytic geometry over non-{A}rchimedean + fields}, + year = {1990}, + volume = {33}, + series = {Mathematical Surveys and Monographs}, + address = {Providence, RI}, + isbn = {0-8218-1534-2}, + mrclass = {32P05 (32C15 32C37 46S10 47S10)}, + mrnumber = {MR1070709 (91k:32038)}, + mrreviewer = {W. Bartenwerfer}, + pages = {x+169}, + publisher = {American Mathematical Society} +} + +@article{BoCa, + author = {Boutot, J.-F. and Carayol, H.}, + title = {Uniformisation {$p$}-adique des courbes de {S}himura: les + th\'eor\`emes de \v {C}erednik et de {D}rinfel\cprime d}, + journal = {Ast\'erisque}, + year = {1991}, + number = {196-197}, + pages = {7, 45--158 (1992)}, + note = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)}, + fjournal = {Ast\'erisque}, + issn = {0303-1179}, + mrclass = {11G18 (14G20 14G35)}, + mrnumber = {MR1141456 (93c:11041)}, + mrreviewer = {Min Ho Lee} +} + +@phdthesis{BradleyPhd, + author = {Bradley, Erik, Patrick}, + title = {$p$-adishe {H}urwitzr\"aume}, + school = {Universit\"at Karlsruhe}, + year = {2002}, + +} + +@article{JoLi, + author = {Jordan, Bruce W. and Livn{\'e}, Ron A.}, + title = {Local {D}iophantine properties of {S}himura curves}, + journal = {Math. Ann.}, + year = {1985}, + volume = {270}, + number = {2}, + pages = {235--248}, + coden = {MAANA}, + fjournal = {Mathematische Annalen}, + issn = {0025-5831}, + mrclass = {11G18 (14G20)}, + mrnumber = {MR771981 (86g:11036)}, + mrreviewer = {Thomas Zink} +} + +@article{K, + author = {Kurihara, Akira}, + title = {On some examples of equations defining {S}himura curves and + the {M}umford uniformization}, + journal = {J. Fac. Sci. Univ. Tokyo Sect. IA Math.}, + year = {1979}, + volume = {25}, + number = {3}, + pages = {277--300}, + coden = {JFTMAT}, + fjournal = {Journal of the Faculty of Science. University of Tokyo. + Section IA. Mathematics}, + issn = {0040-8980}, + mrclass = {14H99 (10D25 14G25)}, + mrnumber = {MR523989 (80e:14010)}, + mrreviewer = {J. S. Milne} +} + +@book{Vi, + author = {Vign{\'e}ras, Marie-France}, + title = {Arithm\'etique des alg\`ebres de quaternions}, + year = {1980}, + volume = {800}, + series = {Lecture Notes in Mathematics}, + address = {Berlin}, + isbn = {3-540-09983-2}, + mrclass = {12A80 (16A18)}, + mrnumber = {MR580949 (82i:12016)}, + mrreviewer = {J. H. H. Chalk}, + pages = {vii+169}, + publisher = {Springer} +} + +@article{KoJPAA06, + author = {Kontogeorgis, Aristides}, + title = {{Polydifferentials and the deformation functor of curves with automorphisms}}, + journal = {Journal of Pure and Applied Algebra}, + year = 2007, + volume = {210}, + number = 2, + pages = {551--558}, + file = {/media/KINGSTON-1/Papers/pdf/KoJPAA07.pdf}, + publisher = {Elsevier} +} + +@article{bhuggins, + author = {Bonnie Huggins}, + title = {Fields of Moduli of Hyperelliptic curves}, + journal = {Math. Res. Lett}, + year = {2007}, + volume = {14}, + number = {00}, + pages = {10001--10014}, + +} + +@incollection{GeerCycles, + author = {van der Geer, Gerard}, + title = {Cycles on the moduli space of abelian varieties}, + booktitle = {Moduli of curves and abelian varieties}, + pages = {65--89}, + publisher = {Vieweg}, + year = {1999}, + series = {Aspects Math., E33}, + address = {Braunschweig}, + mrclass = {14C15 (14K10)}, + mrnumber = {MR1722539 (2001b:14009)} +} + +@article{GZ, + author = {R.\ M.\ Guralnick and M.\ E.\ Zieve}, + title = {Workshop on {\em Automorphisms of Ordinary Curves}, in preparation (Talk in Leiden, Workshop on Automorphism of Curves, 18-08-2004)}, + year = 2004, + +} + +@incollection{OortStrata, + author = {Oort, Frans}, + title = {A stratification of a moduli space of polarized abelian varieties in positive characteristic}, + booktitle = {Moduli of curves and abelian varieties}, + pages = {47--64}, + publisher = {Vieweg}, + year = 1999, + series = {Aspects Math., E33}, + address = {Braunschweig}, + mrclass = {14K10 (14K15)}, + mrnumber = {MR1722538 (2001m:14065)}, + mrreviewer = {Antoine Chambert-Loir} +} + + +@article{katz1972asd, + author = {Katz, N.M.}, + title = {{Algebraic solutions of differential equations (p-curvature and the Hodge filtration)}}, + journal = {Inventiones Mathematicae}, + year = 1972, + volume = {18}, + number = 1, + pages = {1--118}, + file = {/media/KINGSTON/Papers/pdf/Katz72.pdf}, + publisher = {Springer} +} + +@article{jorgenson2000bfs, + author = {Jorgenson, J. and Kramer, J.}, + title = {{Bounds on Faltings’ s delta function through covers}}, + journal = {Preprint}, + year = 2000, + file = {/media/KINGSTON/Papers/pdf/JorgensonKramerFinal.pdf}, + +} + +@article{Schertz2002, + author = {Schertz, R.}, + title = {{Weber's class invariants revisited}}, + journal = {Journal de th{\'e}orie des nombres de Bordeaux}, + year = 2002, + volume = {14}, + number = 1, + pages = {325--343}, + file = {/media/KINGSTON/Papers/pdf/schertz.djvu}, + +} + +@article{waterhouse1969avo, + author = {Waterhouse, W.C.}, + title = {{Abelian varieties over finite fields}}, + journal = {Annales Scientifiques de l'{\'E}cole Normale Sup{\'e}rieure S{\'e}r. 4}, + year = 1969, + volume = {2}, + number = 4, + pages = {521--560}, + file = {/media/KINGSTON/Papers/pdf/whaterhousefinabel.pdf}, + +} + +@book {Wein, + AUTHOR = {Weintraub, Steven H.}, + TITLE = {Representation theory of finite groups: algebra and + arithmetic}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {59}, + PUBLISHER = {American Mathematical Society}, + ADDRESS = {Providence, RI}, + YEAR = {2003}, + PAGES = {x+212}, + ISBN = {0-8218-3222-0}, + MRCLASS = {20C15 (20C20)}, + MRNUMBER = {MR1984740 (2004k:20023)}, +MRREVIEWER = {Jon F. Carlson}, +} + +@article{MR1670658, + author = {Harbater, David and Stevenson, Katherine F.}, + title = {Patching and thickening problems}, + journal = {J. Algebra}, + year = 1999, + volume = {212}, + number = 1, + pages = {272--304}, + file = {/media/KINGSTON/Papers/pdf/PatchThick.pdf}, + comment = {This paper provides a set of useful tools which facilitate constructions of various types of covers of algebraic curves in the formal geometry context. Let $k$ be a field, and let $X^*$ be a projective curve over a power series ring $k[\![t_1,\cdots,t_n]\!]$ whose special fiber $X$ is degenerate. Then, it is shown that "giving a coherent projective module over $X^*$ is equivalent to giving such modules compatibly on a formal neighborhood of each singular point of the closed fiber, and on the formal thickening along the complement of the singular locus $S$ of $X$" (patching problem). This result refines Theorem 1 of \ref[D. Harbater, Amer. J. Math. 115 (1993), no. 3, 487--508; MR1221836 (94f:14024)]. "Thickening problem" deals with the construction of a projective curve $X^*$ over $k[\![t]\!]$ from its closed fiber $X$ and from complete local thickening near the singular locus $S$ of $X$ with the property that the ring of formal functions along $X-S$ turns to trivial deformation $(X-S)\otimes k[\![ +t]\!]$. The present paper solves in the affirmative the thickening problem "in both the relative and absolute senses", and generalizes Grothendieck's result for the case when $X$ is smooth. These tools are applied for the thickening constructions of certain $G$-Galois covers ($G$ denotes a finite group), admissible covers with prescribed behaviors in a formal neighborhood of the singular locus. In particular, Raynaud's rigid analytic result (Theorem 2.2.3 of \ref[Invent. Math. 116 (1994), no. 1-3, 425--462; MR1253200 (94m:14034)]) of constructing a $G$-Galois cover of $\bold P^1$ from $G_i$-Galois covers of $\bold P^1$ (where $G$ is generated by the subgroups $G_1,\cdots,G_n$) can also be proved in the formal geometry context over "large base fields". Applications are also given for the constructions of certain finite quotients of the fundamental groups of curves in characteristic $p>0$.}, + coden = {JALGA4}, + fjournal = {Journal of Algebra}, + issn = {0021-8693}, + mrclass = {14B10 (12F12 14B12 14H30)}, + mrnumber = {MR1670658 (2000b:14004)}, + mrreviewer = {Hiroaki Nakamura} +} +@article {ManinDrinfeld, + AUTHOR = {Manin, Yu. and Drinfeld, V.}, + TITLE = {Periods of {$p$}-adic {S}chottky groups}, + NOTE = {Collection of articles dedicated to Helmut Hasse on his + seventy-fifth birthday}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {262/263}, + YEAR = {1973}, + PAGES = {239--247}, + ISSN = {0075-4102}, + MRCLASS = {14H15 (14K20)}, + MRNUMBER = {0396582 (53 \#444)}, +MRREVIEWER = {T. Oda}, +} + +@article {KockF, + AUTHOR = {Bernhard K\"ock}, + TITLE = {Faithful action on the space of global differentials of an algebraic curve}, + JOURNAL = {arXiv:0911.0625}, + YEAR = {2009}, + +} + +@article {KuzPav, + AUTHOR = {Kuzmanovich, James and Pavlichenkov, Andrey}, + TITLE = {Finite groups of matrices whose entries are integers}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {The American Mathematical Monthly}, + VOLUME = {109}, + YEAR = {2002}, + NUMBER = {2}, + PAGES = {173--186}, + ISSN = {0002-9890}, + CODEN = {AMMYAE}, + MRCLASS = {20G30 (15A36)}, + MRNUMBER = {1903154 (2003c:20057)}, +MRREVIEWER = {Jian Bei An}, + DOI = {10.2307/2695329}, + URL = {http://dx.doi.org/10.2307/2695329}, +} + +@article {FriedSh, + AUTHOR = {Friedland, Shmuel}, + TITLE = {The maximal orders of finite subgroups in {${\rm GL}_n({\bf + Q})$}}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {125}, + YEAR = {1997}, + NUMBER = {12}, + PAGES = {3519--3526}, + ISSN = {0002-9939}, + CODEN = {PAMYAR}, + MRCLASS = {20G05 (20C10 20G30 20H25)}, + MRNUMBER = {1443385 (98b:20064)}, +MRREVIEWER = {Alexander Zimmermann}, + DOI = {10.1090/S0002-9939-97-04283-4}, + URL = {http://dx.doi.org/10.1090/S0002-9939-97-04283-4}, +} + + +@article {FoxI, + AUTHOR = {Fox, Ralph H.}, + TITLE = {Free differential calculus. {I}. {D}erivation in the free + group ring}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {57}, + YEAR = {1953}, + PAGES = {547--560}, + ISSN = {0003-486X}, + MRCLASS = {20.0X}, + MRNUMBER = {0053938 (14,843d)}, +MRREVIEWER = {R. Bott}, +} + @article {ValMaddenReal, + AUTHOR = {Madden, Daniel J. and Valentini, Robert C.}, + TITLE = {The group of automorphisms of algebraic function fields}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {343}, + YEAR = {1983}, + PAGES = {162--168}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {11R32 (14H05)}, + MRNUMBER = {705883 (85i:11096)}, +MRREVIEWER = {Jack Sonn}, + DOI = {10.1515/crll.1983.343.162}, + URL = {http://dx.doi.org/10.1515/crll.1983.343.162}, +} + +@article {CKK-israel, + AUTHOR = {Cornelissen, Gunther and Kato, Fumiharu and Kontogeorgis, + Aristides}, + TITLE = {The relation between rigid-analytic and algebraic deformation + parameters for {A}rtin-{S}chreier-{M}umford curves}, + JOURNAL = {Israel J. Math.}, + FJOURNAL = {Israel Journal of Mathematics}, + VOLUME = {180}, + YEAR = {2010}, + PAGES = {345--370}, + ISSN = {0021-2172}, + CODEN = {ISJMAP}, + MRCLASS = {14G22 (11G05)}, + MRNUMBER = {2735069 (2011j:14054)}, +MRREVIEWER = {Noriko Yui}, + DOI = {10.1007/s11856-010-0107-9}, + URL = {http://dx.doi.org/10.1007/s11856-010-0107-9}, +} + + +@article {KockKonto, + AUTHOR = {K\"ock, Bernhard and Kontogeorgis, Aristides}, + TITLE = {Quadratic differentials and equivariant deformation theory of + curves}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {62}, + YEAR = {2012}, + NUMBER = {3}, + PAGES = {1015--1043}, + ISSN = {0373-0956}, + MRCLASS = {14H30 (11R32 14D15 14F10)}, + MRNUMBER = {3013815}, +MRREVIEWER = {Dmitry Kerner}, + URL = {https://doi.org/10.5802/aif.2715}, +} + + + +@book {Evens, + AUTHOR = {Evens, Leonard}, + TITLE = {The cohomology of groups}, + SERIES = {Oxford Mathematical Monographs}, + NOTE = {Oxford Science Publications}, + PUBLISHER = {The Clarendon Press Oxford University Press}, + ADDRESS = {New York}, + YEAR = {1991}, + PAGES = {xii+159}, + ISBN = {0-19-853580-5}, + MRCLASS = {20J06 (20-02)}, + MRNUMBER = {1144017 (93i:20059)}, +MRREVIEWER = {U. Stammbach}, +} + +@book {BensonNewBook, +AUTHOR = {Benson, Dave}, + TITLE = {Representations of Elementary Abelian p-Groups and Vector Bundles}, + SERIES = {}, + NOTE = {In preparation}, + PUBLISHER = {}, + ADDRESS = {}, + YEAR = {}, + PAGES = {220}, + ISBN = {}, + MRCLASS = {}, + MRNUMBER = {}, +MRREVIEWER = {}, +} + +@book {benson, + AUTHOR = {Benson, D. J.}, + TITLE = {Representations and cohomology. {I}}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {30}, + EDITION = {Second}, + NOTE = {Basic representation theory of finite groups and associative + algebras}, + PUBLISHER = {Cambridge University Press}, + ADDRESS = {Cambridge}, + YEAR = {1998}, + PAGES = {xii+246}, + ISBN = {0-521-63653-1}, + MRCLASS = {20-02 (20Cxx 20J06)}, + MRNUMBER = {1644252 (99f:20001a)}, +} + + @article {CK-Crelle, + AUTHOR = {Cornelissen, Gunther and Kato, Fumiharu}, + TITLE = {Zur {E}ntartung schwach verzweigter {G}ruppenoperationen auf + {K}urven}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {589}, + YEAR = {2005}, + PAGES = {201--236}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {14H37 (14E22)}, + MRNUMBER = {2194683 (2007k:14058)}, + DOI = {10.1515/crll.2005.2005.589.201}, + URL = {http://dx.doi.org/10.1515/crll.2005.2005.589.201}, + } + +@article {CK-Proc, + AUTHOR = {Cornelissen, Gunther and Kato, Fumiharu}, + TITLE = {Mumford curves with maximal automorphism group}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {132}, + YEAR = {2004}, + NUMBER = {7}, + PAGES = {1937--1941 (electronic)}, + ISSN = {0002-9939}, + CODEN = {PAMYAR}, + MRCLASS = {14H37 (14G20)}, + MRNUMBER = {2053963 (2006a:14048)}, + DOI = {10.1090/S0002-9939-04-07379-4}, + URL = {http://dx.doi.org/10.1090/S0002-9939-04-07379-4}, + } + +@article {Kont-Bord, +AUTHOR = {Kontogeorgis, Aristides}, + TITLE = {Field of moduli versus field of definition for cyclic covers + of the projective line}, + JOURNAL = {J. Th\'eor. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux}, + VOLUME = {21}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {679--692}, + ISSN = {1246-7405}, + MRCLASS = {14H37 (14H30)}, + MRNUMBER = {2605539 (2011b:14065)}, +MRREVIEWER = {Meirav Topol}, + URL = {http://jtnb.cedram.org/item?id=JTNB_2009__21_3_679_0} +} + +@article {matlift, +AUTHOR = {Matignon, Michel}, + TITLE = {Lifting the curve $(X^p -X)(Y^p - Y) = 1$ and its automorphism group}, + JOURNAL = {Note non destin\'ee \`a publication, 18-09-2003, + \url{http://www.math.u-bordeaux1.fr/~matignon}}, + URL = {http://www.math.u-bordeaux1.fr/~matignon} +} + + + + +@ARTICLE{Burns, + title = "Maximal order abelian subgroups of symmetric groups", + author = "Burns, JM and Goldsmith, B", + abstract = "This Article is brought to you for free and open access by the + School of Mathematics at ARROW@ DIT. It has been accepted for + inclusion in Articles by an authorized administrator of ARROW@ + DIT. For more information, please contact yvonne. desmond@ dit. + ie, arrow. ...", + publisher = "arrow.dit.ie", + year = 1989, + url = "http://arrow.dit.ie/cgi/viewcontent.cgi?article=1013&context=scschmatart" +} + + + +@ARTICLE{Fuertes2013-in, + title = "Automorphisms group of generalized {F}ermat curves of type", + author = "Fuertes, Yolanda and Gonz\'{a}lez-Diez, Gabino and Hidalgo, + Rub\'{e}n A and Leyton, Maximiliano", + journal = "J. Pure Appl. Algebra", + volume = 217, + number = 10, + pages = "1791--1806", + month = oct, + year = 2013, + url = "http://dx.doi.org/10.1016/j.jpaa.2012.12.014", + issn = "0022-4049", + doi = "10.1016/j.jpaa.2012.12.014" +} + + +@ARTICLE{Gonzalez-Diez2009-md, + title = "Generalized {F}ermat curves", + author = "Gonz\'{a}lez-Diez, Gabino and Hidalgo, Rub\'{e}n A. and Leyton, + Maximiliano", + journal = "J. Algebra", + volume = 321, + number = 6, + pages = "1643--1660", + month = "15~" # mar, + year = 2009, + url = "http://dx.doi.org/10.1016/j.jalgebra.2009.01.002", + keywords = "Riemann surfaces; Fuchsian groups; Automorphisms", + issn = "0021-8693", + doi = "10.1016/j.jalgebra.2009.01.002" +} + + +@ARTICLE{Kontogeorgis2002-to, + title = "Automorphisms of {F}ermat-like varieties", + author = "Kontogeorgis, Aristides", + abstract = "We study the automorphisms of some nice hypersurfaces and + complete intersections in projective space by reducing the + problem to the determination of the linear automorphisms of the + ambient space that leave the algebraic set invariant", + journal = "Manuscripta Math.", + volume = 107, + number = 2, + pages = "187--205", + month = feb, + year = 2002, + url = "http://dx.doi.org/10.1007/s002290100233", + issn = "0025-2611", + doi = "10.1007/s002290100233" +} + + +@ARTICLE{Ihara1985-it, + AUTHOR = {Ihara, Yasutaka}, + TITLE = {Profinite braid groups, {G}alois representations and complex + multiplications}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {123}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {43--106}, + ISSN = {0003-486X}, + MRCLASS = {11G25 (14K22 20E18)}, + MRNUMBER = {825839}, +MRREVIEWER = {David Goss}, + DOI = {10.2307/1971352}, + URL = {https://doi.org/10.2307/1971352}, +} + + + +@ARTICLE{Deligne1980-ep, + title = "La conjecture de Weil. {II}", + author = "Deligne, P", + abstract = "Dans [I], cit6 I par la suite, nous avons ddmontrfi la + conjecture de Weil donnant la valeur absolue complexe des + valeurs propres de Frobenius agissant sur la cohomologie d'une + vari~ t6 projective et lisse d6finie sur un corps fini. Nous~ + tudions ici la cohomologie ...", + journal = "Publications math\'{e}matiques de l'IH\'{E}S", + publisher = "Springer", + year = 1980, + url = "http://www.springerlink.com/index/1731837462H66R10.pdf" +} + +@ARTICLE{Deligne1974-ds, + title = "La conjecture de Weil. {I}", + author = "Deligne, P", + abstract = "Dans cet article, je d6montre la conjecture de Well sur les + valeurs propres des endomorphismes de Frobenius. Un~ nonc~ + precis est donn~ en (I. 6). J'ai tent6 de presenter la + dfimonstration sous une forme aussi g6om6trique et 616mentaire + que possible et j'ai ...", + journal = "Publications Math\'{e}matiques de l'Institut des Hautes", + publisher = "Springer", + year = 1974, + url = "http://link.springer.com/article/10.1007/BF02684373" +} + + +@ARTICLE{Chao_Li_undated-kq, + title = "{KNOTS} {AND} {PRIMES}", + author = "Chao Li, Charmaine Sia", + journal = "Tutorial, Summer 2012", + url = "http://www.math.harvard.edu/~sia/notes/knots_and_primes.pdf" +} + + + +@BOOK{Morishita2011-yw, + title = "Knots and Primes: An Introduction to Arithmetic Topology", + author = "Morishita, M", + publisher = "Springer-Verlag London Limited", + series = "SpringerLink : B{\"{u}}cher", + year = 2011, + url = "http://books.google.gr/books?id=DOnkGOTnI78C", + isbn = "9781447121589", + lccn = "2011940954" +} + +@BOOK{Kohno2006-db, + title = "Primes and Knots", + author = "Kohno, T and Morishita, M and Institute, J.u.s.m.", + publisher = "American Mathematical Society", + number = "$\textbackslash{}tau$. 13", + series = "Contemporary mathematics - American Mathematical Society", + year = 2006, + url = "http://books.google.gr/books?id=htTjE4NmWUcC", + isbn = "9780821857465", + lccn = "2006040609" +} + +@ARTICLE{Morishita2005-jx, + title = "On analogies between primes and knots", + author = "Morishita, M", + journal = "Preprint", + year = 2005 +} + + +@ARTICLE{Tits1956-wj, + title = "Sur les analogues alg\'{e}briques des groupes semi-simples + complexes", + author = "Tits, J", + journal = "Colloque d'algebre sup\'{e}rieure, Bruxelles", + year = 1956 +} + + +@ARTICLE{Kapranov1995-xx, + title = "Cohomology determinants and reciprocity laws", + author = "Kapranov, MM and Smirnov, A", + publisher = "Inst. f{\"{u}}r Experimentelle Mathematik", + year = 1995 +} + + +@ARTICLE{manin2014, + title = "Local zeta factors and geometries under Spec {Z}", + author = "Manin, Yuri I", + abstract = "The first part of this note shows that the odd period + polynomial of each Hecke cusp eigenform for full modular + group produces via Rodriguez--Villegas transform ([Ro--V]) a + polynomial satisfying the functional equation of zeta type + and having nontrivial zeros only on the middle line of its + critical strip. The second part discusses Chebyshev + lambda--structure of the polynomial ring as Borger's descent + data to $\textbackslash{}bold\{F\}_1$ and suggests its role + in possible relation of + $\textbackslash{}Gamma_\{\textbackslash{}bold\{R\}\}$--factor + to {"}real geometry over $\textbackslash{}bold\{F\}_1${"} + (cf. also [CoCons2]).", + journal = "arXiv [math.AG]", + month = "18~" # jul, + year = 2014, + url = "http://arxiv.org/abs/1407.4969", + archivePrefix = "arXiv", + eprint = "1407.4969", + primaryClass = "math.AG", + arxivid = "1407.4969" +} + + +@ARTICLE{Manin2010-od, + title = "Cyclotomy and analytic geometry over {F1}", + author = "Manin, Y", + abstract = "Abstract. Geometry over non-existent ??eld with one element? F1 + conceived by Jacques Tits [Ti] half a century ago recently found + an incarnation, in several related but di?erent guises. In this + paper I analyze the crucial role of roots of unity in this + geometry and propose a ...", + journal = "Quanta of Maths. Conference in honour of Alain", + publisher = "books.google.com", + year = 2010, + url = "http://books.google.com/books?hl=en&lr=&id=8J2au7luwMAC&oi=fnd&pg=PA385&dq=Cyclotomy+analytic+geometry+over+Manin&ots=6o361ULrgY&sig=88FmPcQ9KvW9SNqKVvXQmpnL_9M" +} + + +@UNPUBLISHED{Pena2009-hf, + title = "Mapping {F\_1-land:An} overview of geometries over the field + with one element", + author = "Pe\~{n}a, Javier L\'{o}pez and Lorscheid, Oliver", + abstract = "This paper gives an overview of the various approaches + towards F\_1-geometry. In a first part, we review all known + theories in literature so far, which are: Deitmar's + F\_1-schemes, To\textbackslash{}{"}en and + Vaqui\textbackslash{}'e's F\_1-schemes, Haran's F-schemes, + Durov's generalized schemes, Soul\textbackslash{}'e's + varieties over F\_1 as well as his and Connes-Consani's + variations of this theory, Connes and Consani's + F\_1-schemes, the author's torified varieties and Borger's + Lambda-schemes. In a second part, we will tie up these + different theories by describing functors between the + different F\_1-geometries, which partly rely on the work of + others, partly describe work in progress and partly gain new + insights in the field. This leads to a commutative diagram + of F\_1-geometries and functors between them that connects + all the reviewed theories. We conclude the paper by + reviewing the second author's constructions that lead to + realization of Tits' idea about Chevalley groups over F\_1.", + journal = "arXiv [math.AG]", + month = "1~" # sep, + year = 2009, + url = "http://arxiv.org/abs/0909.0069", + archivePrefix = "arXiv", + eprint = "0909.0069", + primaryClass = "math.AG", + arxivid = "0909.0069" +} + +@ARTICLE{Lorscheid2012-ou, + title = "The geometry of blueprints: Part I: Algebraic background and + scheme theory", + author = "Lorscheid, Oliver", + abstract = "In this paper, we introduce the category of blueprints, which is + a category of algebraic objects that include both commutative + (semi)rings and commutative monoids. This generalization allows a + simultaneous treatment of ideals resp. congruences for rings and + monoids and leads to a common scheme theory. In particular, it + bridges the gap between usual schemes and F 1 -schemes (after + Kato, Deitmar and Connes-Consani). Beside this unification, the + category of blueprints contains new interesting objects as + ?improved? cyclotomic field extensions F 1 n of F 1 and + ?archimedean valuation rings?. It also yields a notion of + semiring schemes. This first paper lays the foundation for + subsequent projects, which are devoted to the following problems: + Tits¢ idea of Chevalley groups over F 1 , congruence schemes, + sheaf cohomology, K-theory and a unified view on analytic + geometry over F 1 , adic spaces (after Huber), analytic spaces + (after Berkovich) and tropical geometry.", + journal = "Adv. Math.", + volume = 229, + number = 3, + pages = "1804--1846", + month = feb, + year = 2012, + url = "http://dx.doi.org/10.1016/j.aim.2011.12.018", + keywords = "Monoids; Semirings; F 1 -geometry; Congruences; Schemes", + issn = "0001-8708", + doi = "10.1016/j.aim.2011.12.018" +} + +@UNPUBLISHED{Lorscheid2012-ff, + title = "The geometry of blueprints. Part {II}: {Tits-Weyl} models of + algebraic groups", + author = "Lorscheid, Oliver", + abstract = "This paper is dedicated to a problem raised by Jacquet Tits + in 1956: the Weyl group of a Chevalley group should find an + interpretation as a group over what is nowadays called + $\textbackslash{}mathbbF_1$, \textbackslash{}emphthe field + with one element. Based on Part I of The geometry of + blueprints, we introduce the class of + \textbackslash{}emphTits morphisms between blue schemes. The + resulting \textbackslash{}emph\{Tits category\} + $\textbackslash{}textup\{Sch\}_\textbackslash{}mathcal\{T\}$ + comes together with a base extension to (semiring) schemes + and the so-called \textbackslash{}emph\{Weyl extension\} to + sets. We prove for $\textbackslash{}mathcal\{G\}$ in a wide + class of Chevalley groups---which includes the special and + general linear groups, symplectic and special orthogonal + groups, and all types of adjoint groups---that a linear + representation of $\textbackslash{}mathcal\{G\}$ defines a + model $G$ in + $\textbackslash{}textup\{Sch\}_\textbackslash{}mathcal\{T\}$ + whose Weyl extension is the Weyl group $W$ of + $\textbackslash{}mathcal\{G\}$. We call such models + \textbackslash{}emph\{Tits-Weyl models\}. The potential of + Tits-Weyl models lies in \textbackslash{}textit\{(a)\} their + intrinsic definition that is given by a linear + representation; \textbackslash{}textit\{(b)\} the (yet to be + formulated) unified approach towards thick and thin + geometries; and \textbackslash{}textit\{(c)\} the extension + of a Chevalley group to a functor on blueprints, which makes + it, in particular, possible to consider Chevalley groups + over semirings. This opens applications to idempotent + analysis and tropical geometry.", + journal = "arXiv [math.AG]", + month = 01, + year = 2012, + url = "http://arxiv.org/abs/1201.1324", + archivePrefix = "arXiv", + eprint = "1201.1324", + primaryClass = "math.AG", + arxivid = "1201.1324" +} + + + +@ARTICLE{Deitmar2005-bn, + title = "Schemes over\textbackslash{} mathbb {F} \_1", + author = "Deitmar, A", + abstract = "Jacques Tits wondered in [5] if there would exist a ?field of + one element''F1 such that for a Chevalley group G one has G(F1) + = W, the Weyl group of G. Recall the Weyl group is defined as W + = N (T )/Z(T ) where T is a maximal torus, N (T ) and Z(T ) are + the normalizer and the ...", + journal = "Number fields and function fields-two parallel worlds", + publisher = "Springer", + year = 2005, + url = "http://link.springer.com/content/pdf/10.1007/0-8176-4447-4_6.pdf" +} + + +@ARTICLE{Connes_undated-pi, + AUTHOR = {Connes, Alain and Consani, Caterina and Marcolli, Matilde}, + TITLE = {Fun with {$\Bbb F_1$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {129}, + YEAR = {2009}, + NUMBER = {6}, + PAGES = {1532--1561}, + ISSN = {0022-314X}, + CODEN = {JNUTA9}, + MRCLASS = {14G15 (11M26 11M55 46L55)}, + MRNUMBER = {2521492 (2010h:14035)}, +MRREVIEWER = {Javier L{\'o}pez Pe{\~n}a}, + DOI = {10.1016/j.jnt.2008.08.007}, + URL = {http://dx.doi.org/10.1016/j.jnt.2008.08.007}, +} + + + + + + +@ARTICLE{Connes703-vf, + title = "The Weil proof and the geometry of the adeles class space, + preprint", + author = "Connes, A and Consani, C and Marcolli, M", + journal = "arXiv preprint math.NT/0703392", + year = 703 +} + + +@ARTICLE{Reiner1957-sx, + title = "Integral representations of cyclic groups of prime order", + author = "Reiner, Irving", + journal = "Proc. Am. Math. Soc.", + volume = 8, + number = 1, + pages = "142--142", + month = "1~" # jan, + year = 1957, + url = "http://dx.doi.org/10.1090/S0002-9939-1957-0083493-6", + issn = "0002-9939", + doi = "10.1090/S0002-9939-1957-0083493-6" +} + + + + + + +@book {Prasolov97, + AUTHOR = {Prasolov, V. V. and Sossinsky, A. B.}, + TITLE = {Knots, links, braids and 3-manifolds}, + SERIES = {Translations of Mathematical Monographs}, + VOLUME = {154}, + NOTE = {An introduction to the new invariants in low-dimensional + topology, + Translated from the Russian manuscript by Sossinsky + [Sosinski{\u\i}]}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1997}, + PAGES = {viii+239}, + ISBN = {0-8218-0588-6}, + MRCLASS = {57M25 (57M12 57N10)}, + MRNUMBER = {1414898 (98i:57018)}, +MRREVIEWER = {Joanna Kania-Bartoszynska}, +} + + + +@ARTICLE{Juyumaya2007-qu, + title = "p-Adic framed braids", + author = "Juyumaya, J and Lambropoulou, S", + abstract = "In this paper we define the p-adic framed braid group F ? , n , + arising as the inverse limit of the modular framed braids. An + element in F ? , n can be interpreted geometrically as an + infinite framed cabling. F ? , n contains the classical framed + braid group as a dense subgroup. This leads to a set of + topological generators for F ? , n and to approximations for the + p-adic framed braids. We further construct a p-adic + Yokonuma-Hecke algebra Y ? , n ( u ) as the inverse limit of a + family of classical Yokonuma-Hecke algebras. These are quotients + of the modular framed braid groups over a quadratic relation. + Finally, we give topological generators for Y ? , n ( u ) .", + journal = "Topol. Appl.", + volume = 154, + number = 8, + pages = "1804--1826", + month = apr, + year = 2007, + url = "http://dx.doi.org/10.1016/j.topol.2007.01.010", + keywords = "Inverse limits; p-adic integers; p-adic framed braids; p-adic + infinite cablings; p-adic Yokonuma-Hecke algebras; p-adic Markov + traces", + issn = "0166-8641", + doi = "10.1016/j.topol.2007.01.010" +} + +@ARTICLE{Juyumaya2013-nr, + title = "p-adic framed braids {II}", + author = "Juyumaya, Jes\'{u}s and Lambropoulou, Sofia", + abstract = "The Yokonuma-Hecke algebras are quotients of the modular framed + braid group and they support Markov traces. In this paper, which + is sequel to Juyumaya and Lambropoulou (2007) [6], we explore + further the structures of the p -adic framed braids and the p + -adic Yokonuma-Hecke algebras constructed by Juyumaya and + Lambropoulou (2007) [6], by means of dense sub-structures + approximating p -adic elements. We also construct a p -adic + Markov trace on the p -adic Yokonuma-Hecke algebras and + approximate the values of the p -adic trace on p -adic elements. + Surprisingly, the Markov traces do not re-scale directly to yield + isotopy invariants of framed links. This leads to imposing the ¡ + E -condition¢ on the trace parameters. For solutions of the ¡ E + -system¢ we then define 2-variable isotopy invariants of modular + framed links. These lift to p -adic isotopy invariants of + classical framed links. The Yokonuma-Hecke algebras have + topological interpretations in the context of framed knots, of + classical knots of singular knots and of transverse knots.", + journal = "Adv. Math.", + volume = 234, + number = 0, + pages = "149--191", + month = feb, + year = 2013, + url = "http://dx.doi.org/10.1016/j.aim.2012.10.011", + keywords = "p -adic integers; Framed braid; p -adic framed braid; + Yokonuma-Hecke algebra; Markov trace; Framed link; p -adic framed + link; E -condition; E -system; Isotopy invariant", + issn = "0001-8708", + doi = "10.1016/j.aim.2012.10.011" +} + +@article{GuMas, + author = {Goundaroulis D. }, + title = {Arithmetic Topology}, + journal = {Master dissertation University of the Aegean (In Greek)}, + year = {2006}, + +} + + +@UNPUBLISHED{Borger2009-pv, + title = "Lambda-rings and the field with one element", + author = "Borger, James", + abstract = "The theory of Lambda-rings, in the sense of Grothendieck's + Riemann-Roch theory, is an enrichment of the theory of + commutative rings. In the same way, we can enrich usual + algebraic geometry over the ring Z of integers to produce + Lambda-algebraic geometry. We show that Lambda-algebraic + geometry is in a precise sense an algebraic geometry over a + deeper base than Z and that it has many properties predicted + for algebraic geometry over the mythical field with one + element. Moreover, it does this is a way that is both + formally robust and closely related to active areas in + arithmetic algebraic geometry.", + journal = "arXiv [math.NT]", + month = 06, + year = 2009, + url = "http://arxiv.org/abs/0906.3146", + archivePrefix = "arXiv", + eprint = "0906.3146", + primaryClass = "math.NT", + arxivid = "0906.3146" +} + + +@ARTICLE{Habiro2008-ln, + title = "A unified {Witten-Reshetikhin-Turaev} invariant for integral + homology spheres", + author = "Habiro, Kazuo", + abstract = "We construct an invariant J M of integral homology spheres M + with values in a completion + \textbackslash{}(\textbackslash{}widehat\{\textbackslash{}mathbb\{Z\}[q]\}\textbackslash{}) + of the polynomial ring â„?[q] such that the evaluation at each + root of unity ζ gives the the SU(2) Witten-Reshetikhin-Turaev + invariant τζ(M) of M at ζ. Thus J M unifies all the SU(2) + Witten-Reshetikhin-Turaev invariants of M. It also follows that + τζ(M) as a function on ζ behaves like an “analytic function” + defined on the set of roots of unity.", + journal = "Invent. Math.", + publisher = "Springer-Verlag", + volume = 171, + number = 1, + pages = "1--81", + month = "1~" # jan, + year = 2008, + issn_alt = "1432-1297" +} + + +@UNPUBLISHED{Bruyn2013-re, + title = "Absolute geometry and the Habiro topology", + author = "Bruyn, Lieven Le", + abstract = "Lecture notes of a course on A. Smirnov's approach to the + ABC-conjecture via F1-geometry and an attempt to relate this + to Jim Borger's F1-geometry based on lambda-rings.", + journal = "arXiv [math.RA]", + month = 04, + year = 2013, + url = "http://arxiv.org/abs/1304.6532", + archivePrefix = "arXiv", + eprint = "1304.6532", + primaryClass = "math.RA", + arxivid = "1304.6532" +} + +@book {alperin, + AUTHOR = {Alperin, J. L.}, + TITLE = {Local representation theory}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {11}, + NOTE = {Modular representations as an introduction to the local + representation theory of finite groups}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1986}, + PAGES = {x+178}, + ISBN = {0-521-30660-4; 0-521-44926-X}, + MRCLASS = {20-02 (20C20)}, + MRNUMBER = {860771 (87i:20002)}, +MRREVIEWER = {P. Donovan}, + DOI = {10.1017/CBO9780511623592}, + URL = {http://dx.doi.org/10.1017/CBO9780511623592}, +} + + + + +@BOOK{SchneiderModReps, + title = "Modular Representation Theory of Finite Groups", + author = "Schneider, P", + publisher = "Springer", + series = "SpringerLink : B{\"{u}}cher", + year = 2012, + url = "http://books.google.gr/books?id=EJqWGguAMU8C", + isbn = "9781447148326", + lccn = "2012954001" +} + + + +@ARTICLE{OReilly1964-nc, + title = "On the Modular Representation Algebra Metacyclic Groups", + author = "O'Reilly, M F", + journal = "J. Lond. Math. Soc.", + publisher = "Oxford University Press", + volume = 1, + number = 1, + pages = "267--276", + year = 1964, + issn = "0024-6107" +} + + + +@ARTICLE{Srinivasan1960-rk, + title = "On the indecomposable representations of a certain class of + groups", + author = "Srinivasan, Bhama", + journal = "Proc. Lond. Math. Soc.", + publisher = "Citeseer", + volume = 10, + number = 3, + pages = "497--513", + year = 1960, + url = "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.105.1694&rep=rep1&type=pdf", + issn = "0024-6115" +} + + + + +@ARTICLE{Chevalley1934-eb, + title = "{\"{U}}ber das Verhalten der Integrale 1. Gattung bei + Automorphismen des Funktionenk{\"{o}}rpers", + author = "Chevalley, C and Weil, A and Hecke, E", + abstract = ".... In zwei sch(/nen Arbeiten haben Sie die linearen + Substitutions- gruppen bestimmt, die dadureh entstehen, dab man + auf die zur Kon~ gruenzuntergruppe q-ter Stufe der Modulgruppe + geh0rigen Differentiale 1. Gattung die Substitutionen der vollen + Modulgruppe ausfibtl). Dabei ...", + journal = "Abh. Math. Semin. Univ. Hambg.", + publisher = "Springer", + year = 1934, + url = "http://www.springerlink.com/index/R1M8724400M1N356.pdf", + issn = "0025-5858" +} + +@book{suzuki1982group, + title={Group theory}, + author={Suzuki, M.}, + number={$\tau$. 1}, + isbn={9783540109150}, + lccn={81009159}, + series={Grundlehren der mathematischen Wissenschaften}, + url={https://books.google.gr/books?id=xATvAAAAMAAJ}, + year={1982}, + publisher={Springer-Verlag} +} + + +@book{moreno1993algebraic, +author = {Moreno, C}, +title = {{Algebraic Curves Over Finite Fields}}, +publisher = {Cambridge University Press}, +year = {1993}, +series = {Cambridge Tracts in Mathematics} +} + + +@article {Natan2002, + AUTHOR = {Bar-Natan, Dror}, + TITLE = {On {K}hovanov's categorification of the {J}ones polynomial}, + JOURNAL = {Algebr. Geom. Topol.}, + FJOURNAL = {Algebraic \& Geometric Topology}, + VOLUME = {2}, + YEAR = {2002}, + PAGES = {337--370 (electronic)}, + ISSN = {1472-2747}, + MRCLASS = {57M27}, + MRNUMBER = {1917056 (2003h:57014)}, +MRREVIEWER = {Jacob Andrew Rasmussen}, + DOI = {10.2140/agt.2002.2.337}, + URL = {http://dx.doi.org/10.2140/agt.2002.2.337}, +} + + + + +@INCOLLECTION{Bodigheimer2012-gr, + title = "Embeddings of braid groups into mapping class groups and their + homology", + booktitle = "Configuration Spaces", + author = "B{\"{o}}digheimer, Carl-Friedrich and Tillmann, Ulrike", + publisher = "Scuola Normale Superiore", + pages = "173--191", + series = "CRM Series", + year = 2012 +} + + +@INPROCEEDINGS{Birman1971-qj, + title = "On the mapping class groups of closed surfaces as covering + spaces", + booktitle = "Advances in the theory of Riemann surfaces (Proc. Conf., Stony + Brook, {NY}, 1969)", + author = "Birman, Joan S and Hilden, Hugh M", + pages = "81--115", + year = 1971 +} + + + + +@ARTICLE{Birman1972-pg, + title = "Isotopies of homeomorphisms of {R}iemann surfaces and a theorem + about {A}rtin's braid group", + author = "Birman, Joan S and Hilden, Hugh M", + abstract = "Project Euclid - mathematics and statistics online", + journal = "Bull. Am. Math. Soc.", + publisher = "American Mathematical Society", + volume = 78, + number = 6, + pages = "1002--1004", + month = nov, + year = 1972 +} + + +@ARTICLE{Birman1973-ea, + title = "On Isotopies of Homeomorphisms of Riemann Surfaces", + author = "Birman, Joan S and Hilden, Hugh M", + journal = "Ann. Math.", + publisher = "Annals of Mathematics", + volume = 97, + number = 3, + pages = "424--439", + year = 1973 +} + +@article{witt37, +AUTHOR = {Witt, Ernst}, + TITLE = {Treue {D}arstellung {L}iescher {R}inge}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {177}, + YEAR = {1937}, + PAGES = {152--160}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {Contributed Item}, + MRNUMBER = {1581553}, + DOI = {10.1515/crll.1937.177.152}, + URL = {http://dx.doi.org/10.1515/crll.1937.177.152}, +} + + + + + +@incollection {IharaCruz, + AUTHOR = {Ihara, Yasutaka}, + TITLE = {Arithmetic analogues of braid groups and {G}alois + representations}, + BOOKTITLE = {Braids ({S}anta {C}ruz, {CA}, 1986)}, + SERIES = {Contemp. Math.}, + VOLUME = {78}, + PAGES = {245--257}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {1988}, + MRCLASS = {11R32 (14H30 20F28 57M05)}, + MRNUMBER = {975083}, +MRREVIEWER = {B. Heinrich Matzat}, + URL = {https://doi.org/10.1090/conm/078/975083}, +} + +@article {MorishitaATIT, + AUTHOR = {Kodani, Hisatoshi and Morishita, Masanori and Terashima, Yuji}, + TITLE = {Arithmetic {T}opology in {I}hara {T}heory}, + JOURNAL = {Publ. Res. Inst. Math. Sci.}, + FJOURNAL = {Publications of the Research Institute for Mathematical + Sciences}, + VOLUME = {53}, + YEAR = {2017}, + NUMBER = {4}, + PAGES = {629--688}, + ISSN = {0034-5318}, + MRCLASS = {11 (57M27)}, + MRNUMBER = {3716496}, + URL = {https://doi.org/10.4171/PRIMS/53-4-6}, +} + +@book {DDMS, + AUTHOR = {Dixon, J. D. and du Sautoy, M. P. F. and Mann, A. and Segal, + D.}, + TITLE = {Analytic pro-{$p$} groups}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {61}, + EDITION = {Second}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1999}, + PAGES = {xviii+368}, + ISBN = {0-521-65011-9}, + MRCLASS = {20E18 (20G30)}, + MRNUMBER = {1720368}, +MRREVIEWER = {Alexander Lubotzky}, + URL = {https://doi.org/10.1017/CBO9780511470882}, +} + +@book {LangIntroAlgAbFun, + AUTHOR = {Lang, Serge}, + TITLE = {Introduction to algebraic and abelian functions}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {89}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, New York-Berlin}, + YEAR = {1982}, + PAGES = {ix+169}, + ISBN = {0-387-90710-6}, + MRCLASS = {14Hxx (14-01 14K20)}, + MRNUMBER = {681120}, +MRREVIEWER = {Reinhard B\"olling}, +} + +@article {McMullenBraidHodge, + AUTHOR = {McMullen, Curtis T.}, + TITLE = {Braid groups and {H}odge theory}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {355}, + YEAR = {2013}, + NUMBER = {3}, + PAGES = {893--946}, + ISSN = {0025-5831}, + MRCLASS = {20F36 (14C30)}, + MRNUMBER = {3020148}, +MRREVIEWER = {Francesca Vetro}, + URL = {https://doi.org/10.1007/s00208-012-0804-2}, +} + +@article {ChenHomologyOfBraidGroups, + AUTHOR = {Chen, Weiyan}, + TITLE = {Homology of braid groups, the {B}urau representation, and + points on superelliptic curves over finite fields}, + JOURNAL = {Israel J. Math.}, + FJOURNAL = {Israel Journal of Mathematics}, + VOLUME = {220}, + YEAR = {2017}, + NUMBER = {2}, + PAGES = {739--762}, + ISSN = {0021-2172}, + MRCLASS = {20F36 (11G05 14H20 14H50)}, + MRNUMBER = {3666443}, + URL = {https://doi.org/10.1007/s11856-017-1534-7}, +} + +@book {MagKarSol, + AUTHOR = {Magnus, Wilhelm and Karrass, Abraham and Solitar, Donald}, + TITLE = {Combinatorial group theory}, + EDITION = {second}, + NOTE = {Presentations of groups in terms of generators and relations}, + PUBLISHER = {Dover Publications, Inc., Mineola, NY}, + YEAR = {2004}, + PAGES = {xii+444}, + ISBN = {0-486-43830-9}, + MRCLASS = {20E05 (05A15 20E06 20F12)}, + MRNUMBER = {2109550}, +} + + +@article{Hasse1937, +author = {Hasse, H.}, +journal = {Journal für die reine und angewandte {M}athematik}, +keywords = {algebraic function fields; higher differential quotients}, +pages = {215-223}, +title = {Noch eine {B}egründung der {T}heorie der höheren {D}ifferentialquotienten in einem algebraischen {F}unktionenkörper einer {U}nbestimmten. (Nach einer brieflichen {M}itteilung von {F}.{K}. {S}chmidt in {J}ena).}, +url = {http://eudml.org/doc/150015}, +volume = {177}, +year = {1937}, +} + + +@ARTICLE{Schmidt39, + title = "Die {W}ronskische {D}eterminante in beliebigen differenzierbaren + {F}unktionenk{\"{o}}rpern", + author = "Schmidt, Friedrich Karl", + journal = "Math. Z.", + publisher = "Springer-Verlag", + volume = 45, + number = 1, + pages = "62--74", + url = "http://link.springer.com/article/10.1007/BF01580273", + issn = "0025-5874, 1432-1823", + doi = "10.1007/BF01580273" +} + +@book{gelfand2008discriminants, + title={Discriminants, Resultants, and Multidimensional Determinants}, + author={Gelfand, I.M. and Kapranov, M. and Zelevinsky, A.}, + isbn={9780817647704}, + lccn={93046733}, + series={Modern Birkh{\"a}user Classics}, + url={https://books.google.fr/books?id=n6ZxAKevSbsC}, + year={2008}, + publisher={Birkh{\"a}user Boston} +} + + +@ARTICLE{Drinfeld_undated-ko, + title = "Commutative subrings of certain noncommutative rings", + author = "Drinfel'd, V G", + journal = "Funct. Anal. Appl.", + publisher = "Kluwer Academic Publishers-Plenum Publishers", + volume = 11, + number = 1, + pages = "9--12", + url = "http://link.springer.com/article/10.1007/BF01135527", + issn = "0016-2663, 1573-8485", + doi = "10.1007/BF01135527" +} + +@BOOK{Da_Silva2001-jk, + title = "Lectures on Symplectic Geometry", + author = "da Silva, A C", + publisher = "Springer", + series = "Lecture Notes in Mathematics", + year = 2001, + url = "http://books.google.gr/books?id=r9i6pXc7GEQC", + isbn = "9783540421955", + lccn = "2008924358", + edition = {1., st ed. 2001. Corr., 2nd printing}, + volume = {1764} + } + + @article {wal, + AUTHOR = {Wallace, Andrew H.}, + TITLE = {Tangency and duality over arbitrary fields}, + JOURNAL = {Proc. London Math. Soc. (3)}, + FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, + VOLUME = {6}, + YEAR = {1956}, + PAGES = {321--342}, + ISSN = {0024-6115}, + MRCLASS = {14.0X}, + MRNUMBER = {0080354}, +MRREVIEWER = {D. Pedoe}, +} + +@incollection {hefklei, + AUTHOR = {Hefez, Abramo and Kleiman, Steven L.}, + TITLE = {Notes on the duality of projective varieties}, + BOOKTITLE = {Geometry today ({R}ome, 1984)}, + SERIES = {Progr. Math.}, + VOLUME = {60}, + PAGES = {143--183}, + PUBLISHER = {Birkh\"auser Boston, Boston, MA}, + YEAR = {1985}, + MRCLASS = {14N05 (14N10)}, + MRNUMBER = {895153}, +MRREVIEWER = {Susan J. Colley}, +} + + +@article {kaji, + AUTHOR = {Kaji, Hajime}, + TITLE = {On the inseparable degrees of the {G}auss map and the + projection of the conormal variety to the dual of higher order + for space curves}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {292}, + YEAR = {1992}, + NUMBER = {3}, + PAGES = {529--532}, + ISSN = {0025-5831}, + CODEN = {MAANA}, + MRCLASS = {14H60 (14H35 14N05)}, + MRNUMBER = {1152948}, +MRREVIEWER = {Masaaki Homma}, + DOI = {10.1007/BF01444633}, + URL = {http://dx.doi.org/10.1007/BF01444633}, +} + +@incollection {kleipie, + AUTHOR = {Kleiman, Steven and Piene, Ragni}, + TITLE = {On the inseparability of the {G}auss map}, + BOOKTITLE = {Enumerative algebraic geometry ({C}openhagen, 1989)}, + SERIES = {Contemp. Math.}, + VOLUME = {123}, + PAGES = {107--129}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {1991}, + MRCLASS = {14N05 (14M10 14N10)}, + MRNUMBER = {1143550}, +MRREVIEWER = {Susan J. Colley}, + DOI = {10.1090/conm/123/1143550}, + URL = {http://dx.doi.org/10.1090/conm/123/1143550}, +} + +@article {fukkaji, + AUTHOR = {Fukasawa, Satoru and Kaji, Hajime}, + TITLE = {The separability of the {G}auss map and the reflexivity for a + projective surface}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {256}, + YEAR = {2007}, + NUMBER = {4}, + PAGES = {699--703}, + ISSN = {0025-5874}, + CODEN = {MAZEAX}, + MRCLASS = {14N05 (14M15)}, + MRNUMBER = {2308883}, +MRREVIEWER = {Nicolas Perrin}, + DOI = {10.1007/s00209-006-0085-0}, + URL = {http://dx.doi.org/10.1007/s00209-006-0085-0}, +} + + +@book {MatzatMalle, + AUTHOR = {Malle, Gunter and Matzat, B. Heinrich}, + TITLE = {Inverse {G}alois theory}, + SERIES = {Springer Monographs in Mathematics}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1999}, + PAGES = {xvi+436}, + ISBN = {3-540-62890-8}, + MRCLASS = {12F12 (11R32 12F10 14G32 20C33 20F36 20G40)}, + MRNUMBER = {1711577}, +MRREVIEWER = {Helmut V{\"o}lklein}, + DOI = {10.1007/978-3-662-12123-8}, + URL = {http://dx.doi.org/10.1007/978-3-662-12123-8}, +} + +@book {VolkleinGaGG, + AUTHOR = {V{\"o}lklein, Helmut}, + TITLE = {Groups as {G}alois groups}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {53}, + NOTE = {An introduction}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1996}, + PAGES = {xviii+248}, + ISBN = {0-521-56280-5}, + MRCLASS = {12F12}, + MRNUMBER = {1405612}, +MRREVIEWER = {Martin Epkenhans}, + DOI = {10.1017/CBO9780511471117}, + URL = {http://dx.doi.org/10.1017/CBO9780511471117}, +} + +@misc{milneLEC, +author={Milne, James S.}, +title={Lectures on Etale Cohomology (v2.21)}, +year={2013}, +note={Available at www.jmilne.org/math/}, +pages={202} +} + + +@ARTICLE{Hosgood2016-sp, + title = "An introduction to varieties in weighted projective space", + author = "Hosgood, Timothy", + abstract = "Weighted projective space arises when we consider the usual + geometric definition for projective space and allow for + non-trivial weights. On its own, this extra freedom gives + rise to more than enough interesting phenomena, but it is + the fact that weighted projective space arises naturally in + the context of classical algebraic geometry that can be + surprising. Using the Riemann-Roch theorem to calculate + l(E,nD) where E is a non-singular cubic curve inside + projective 2-space and D=p is a point in E we obtain a + non-negatively graded ring R(E) by taking the direct sum of + the L(E,nD) for n greater than or equal to 0. This gives + rise to an embedding of E inside the weighted projective + space P(1,2,3). To understand a space it is always a good + idea to look at the things inside it. The main content of + this paper is the introduction and explanation of many basic + concepts of weighted projective space and its varieties. + There are already many brilliant texts on the topic but none + of them are aimed at an audience with only an + undergraduate's knowledge of mathematics. This paper hopes + to partially fill this gap whilst maintaining a good balance + between 'interesting' and 'simple'. The main result of this + paper is a reasonably simple degree-genus formula for + non-singular 'sufficiently general' plane curves, proved + using not much more than the Riemann-Hurwitz formula.", + month = "8~" # apr, + year = 2016, + url = "http://arxiv.org/abs/1604.02441", + archivePrefix = "arXiv", + eprint = "1604.02441", + primaryClass = "math.AG", + arxivid = "1604.02441" +} + +@article {HiRuKoPa, + AUTHOR = {Hidalgo, Rub\'en A. and Kontogeorgis, Aristides and + Leyton-\'Alvarez, Maximiliano and Paramantzoglou, Panagiotis}, + TITLE = {Automorphisms of generalized {F}ermat curves}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {221}, + YEAR = {2017}, + NUMBER = {9}, + PAGES = {2312--2337}, + ISSN = {0022-4049}, + MRCLASS = {14H37 (14H25 14M10)}, + MRNUMBER = {3631719}, + DOI = {10.1016/j.jpaa.2016.12.011}, + URL = {http://dx.doi.org/10.1016/j.jpaa.2016.12.011}, +} + +@book {CrespoDiff, + AUTHOR = {Crespo, Teresa and Hajto, Zbigniew}, + TITLE = {Algebraic groups and differential {G}alois theory}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {122}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2011}, + PAGES = {xiv+225}, + ISBN = {978-0-8218-5318-4}, + MRCLASS = {12H05 (20G15 34M15 34M50 68W30)}, + MRNUMBER = {2778109}, +MRREVIEWER = {David Bl\'azquez-Sanz}, + DOI = {10.1090/gsm/122}, + URL = {http://dx.doi.org/10.1090/gsm/122}, +} + +@book {NeukirchCohoNumFields, + AUTHOR = {Neukirch, J\"urgen and Schmidt, Alexander and Wingberg, Kay}, + TITLE = {Cohomology of number fields}, + SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {323}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2008}, + PAGES = {xvi+825}, + ISBN = {978-3-540-37888-4}, + MRCLASS = {11R34 (11-02 11G45 11R23 11S20 11S25 11S31 12G05)}, + MRNUMBER = {2392026}, + URL = {https://doi.org/10.1007/978-3-540-37889-1}, +} + +@book {GilleCentralSimpleAlgebras, + AUTHOR = {Gille, Philippe and Szamuely, Tam\'as}, + TITLE = {Central simple algebras and {G}alois cohomology}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {101}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2006}, + PAGES = {xii+343}, + ISBN = {978-0-521-86103-8; 0-521-86103-9}, + MRCLASS = {16K20 (14F22 19C30)}, + MRNUMBER = {2266528}, +MRREVIEWER = {Gr\'egory Berhuy}, + URL = {https://doi.org/10.1017/CBO9780511607219}, +} + +@book {ShafaBo1a, + AUTHOR = {Shafarevich, Igor R.}, + TITLE = {Basic algebraic geometry. 1}, + EDITION = {Second}, + NOTE = {Varieties in projective space, + Translated from the 1988 Russian edition and with notes by + Miles Reid}, + PUBLISHER = {Springer-Verlag}, + ADDRESS = {Berlin}, + YEAR = {1994}, + PAGES = {xx+303}, + ISBN = {3-540-54812-2}, + MRCLASS = {14-01}, + MRNUMBER = {MR1328833 (95m:14001)}, +} +@book {ShafaBo2, + title={Basic Algebraic Geometry 2}, + author={Shafarevich, I.R.}, + isbn={9783540575542}, + lccn={94011903}, + series={Basic Algebraic Geometry}, + url={https://books.google.gr/books?id=jZW2-UW4DkMC}, + year={1994}, + publisher={Springer-Verlag} +} + +@ARTICLE{Karanikolopoulos2013-vg, + AUTHOR = {Karanikolopoulos, Sotiris and Kontogeorgis, Aristides}, + TITLE = {Automorphisms of curves and {W}eierstrass semigroups for + {H}arbater-{K}atz-{G}abber covers}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {371}, + YEAR = {2019}, + NUMBER = {9}, + PAGES = {6377--6402}, + ISSN = {0002-9947}, + MRCLASS = {14H37 (11G20 14H10 14H55 20M14)}, + MRNUMBER = {3937329}, + DOI = {10.1090/tran/7562}, + URL = {https://doi.org/10.1090/tran/7562}, +} + + + +@incollection {PriesFermat, + AUTHOR = {Davis, Rachel and Pries, Rachel and Stojanoska, Vesna and + Wickelgren, Kirsten}, + TITLE = {Galois action on the homology of {F}ermat curves}, + BOOKTITLE = {Directions in number theory}, + SERIES = {Assoc. Women Math. Ser.}, + VOLUME = {3}, + PAGES = {57--86}, + PUBLISHER = {Springer, [Cham]}, + YEAR = {2016}, + MRCLASS = {14H50 (11D41 11R18 14F35 14H25)}, + MRNUMBER = {3596577}, + URL = {https://doi.org/10.1007/978-3-319-30976-7_3}, +} + +@article {AndersonIhara88, + AUTHOR = {Anderson, Greg and Ihara, Yasutaka}, + TITLE = {Pro-{$l$} branched coverings of {${\bf P}^1$} and higher + circular {$l$}-units}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {128}, + YEAR = {1988}, + NUMBER = {2}, + PAGES = {271--293}, + ISSN = {0003-486X}, + MRCLASS = {14H25 (11G20 14H30)}, + MRNUMBER = {960948}, +MRREVIEWER = {David Goss}, + URL = {https://doi.org/10.2307/1971443}, +} + + +@article {AndersonSoliton, + AUTHOR = {Anderson, Greg W.}, + TITLE = {Torsion points on {J}acobians of quotients of {F}ermat curves + and {$p$}-adic soliton theory}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {118}, + YEAR = {1994}, + NUMBER = {3}, + PAGES = {475--492}, + ISSN = {0020-9910}, + MRCLASS = {11G30 (11S99 14H40 58F07)}, + MRNUMBER = {1296355}, +MRREVIEWER = {David Goss}, + URL = {https://doi.org/10.1007/BF01231542}, +} + +@article {AndersonDuke, + AUTHOR = {Anderson, Greg W.}, + TITLE = {Torsion points on {F}ermat {J}acobians, roots of circular + units and relative singular homology}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {54}, + YEAR = {1987}, + NUMBER = {2}, + PAGES = {501--561}, + ISSN = {0012-7094}, + MRCLASS = {14G25 (11G35 11R18 14F35)}, + MRNUMBER = {899404}, +MRREVIEWER = {Yasutaka Ihara}, + URL = {https://doi.org/10.1215/S0012-7094-87-05422-6}, +} + +@Inbook{Antoniadis2017, +author="Antoniadis, Jannis A. +and Kontogeorgis, Aristides", +editor="Lambropoulou, Sofia +and Theodorou, Doros +and Stefaneas, Petros +and Kauffman, Louis H.", +title="Automorphisms of Curves", +bookTitle="Algebraic Modeling of Topological and Computational Structures and Applications: THALES, Athens, Greece, July 1-3, 2015", +year="2017", +publisher="Springer International Publishing", +address="Cham", +pages="339--361", +abstract="This is a survey article concerning the groups of automorphisms of curves defined over algebraically closed fields of positive characteristic, their representations and applications to their deformation theory.", +isbn="978-3-319-68103-0", +doi="10.1007/978-3-319-68103-0_16", +url="https://doi.org/10.1007/978-3-319-68103-0_16" +} + + +@article {KaranProc, + AUTHOR = {Karanikolopoulos, Sotiris and Kontogeorgis, Aristides}, + TITLE = {Integral representations of cyclic groups acting on relative + holomorphic differentials of deformations of curves with + automorphisms}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {142}, + YEAR = {2014}, + NUMBER = {7}, + PAGES = {2369--2383}, + ISSN = {0002-9939}, + MRCLASS = {14H37 (14F10)}, + MRNUMBER = {3195760}, +MRREVIEWER = {Jeroen Sijsling}, + URL = {https://doi.org/10.1090/S0002-9939-2014-12010-7}, +} + +@article {Garcia95, + AUTHOR = {Garcia, Arnaldo and Lax, R. F.}, + TITLE = {On canonical ideals, intersection numbers, and {W}eierstrass + points on {G}orenstein curves}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {178}, + YEAR = {1995}, + NUMBER = {3}, + PAGES = {807--832}, + ISSN = {0021-8693}, + MRCLASS = {14H20 (14B05 14H55)}, + MRNUMBER = {1364344}, +MRREVIEWER = {Takao Kato}, + URL = {https://doi.org/10.1006/jabr.1995.1379}, +} + +@article {Saint-Donat73, + AUTHOR = {Saint-Donat, B.}, + TITLE = {On {P}etri's analysis of the linear system of quadrics through + a canonical curve}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {206}, + YEAR = {1973}, + PAGES = {157--175}, + ISSN = {0025-5831}, + MRCLASS = {14H45 (14J25)}, + MRNUMBER = {0337983}, +MRREVIEWER = {H. H. Martens}, + URL = {https://doi.org/10.1007/BF01430982}, +} + +@article {MR3106737, + AUTHOR = {Contiero, Andr\'e and St\"ohr, Karl-Otto}, + TITLE = {Upper bounds for the dimension of moduli spaces of curves with + symmetric {W}eierstrass semigroups}, + JOURNAL = {J. Lond. Math. Soc. (2)}, + FJOURNAL = {Journal of the London Mathematical Society. Second Series}, + VOLUME = {88}, + YEAR = {2013}, + NUMBER = {2}, + PAGES = {580--598}, + ISSN = {0024-6107}, + MRCLASS = {14H10 (14H20 14H55)}, + MRNUMBER = {3106737}, +MRREVIEWER = {Aristides I. Kontogeorgis}, + URL = {https://doi.org/10.1112/jlms/jdt034}, +} + + +@article {MR1228616, + AUTHOR = {St\"ohr, Karl-Otto}, + TITLE = {On the moduli spaces of {G}orenstein curves with symmetric + {W}eierstrass semigroups}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {441}, + YEAR = {1993}, + PAGES = {189--213}, + ISSN = {0075-4102}, + MRCLASS = {14H10 (14H45)}, + MRNUMBER = {1228616}, +MRREVIEWER = {Allen Tannenbaum}, +} + +@article {Obus2017, + AUTHOR = {Obus, Andrew}, + TITLE = {A generalization of the {O}ort conjecture}, + JOURNAL = {Comment. Math. Helv.}, + FJOURNAL = {Commentarii Mathematici Helvetici. A Journal of the Swiss + Mathematical Society}, + VOLUME = {92}, + YEAR = {2017}, + NUMBER = {3}, + PAGES = {551--620}, + ISSN = {0010-2571}, + MRCLASS = {14H37 (11G20 12F10 12F15 13F35 14G17 14G22)}, + MRNUMBER = {3682780}, + URL = {https://doi.org/10.4171/CMH/419}, +} + +@article {ObusWewers, + AUTHOR = {Obus, Andrew and Wewers, Stefan}, + TITLE = {Cyclic extensions and the local lifting problem}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {180}, + YEAR = {2014}, + NUMBER = {1}, + PAGES = {233--284}, + ISSN = {0003-486X}, + MRCLASS = {11G30 (11G20 11S15 14H25)}, + MRNUMBER = {3194815}, +MRREVIEWER = {Kevin P. Keating}, + URL = {https://doi.org/10.4007/annals.2014.180.1.5}, +} + + +@incollection {Obus12, + AUTHOR = {Obus, Andrew}, + TITLE = {The (local) lifting problem for curves}, + BOOKTITLE = {Galois-{T}eichm\"uller theory and arithmetic geometry}, + SERIES = {Adv. Stud. Pure Math.}, + VOLUME = {63}, + PAGES = {359--412}, + PUBLISHER = {Math. Soc. Japan, Tokyo}, + YEAR = {2012}, + MRCLASS = {14H37 (11G20 14G17)}, + MRNUMBER = {3051249}, +MRREVIEWER = {Jeroen Sijsling}, +} + +@incollection {MR3971180, + AUTHOR = {Obus, Andrew}, + TITLE = {Lifting of curves with automorphisms}, + BOOKTITLE = {Open problems in arithmetic algebraic geometry}, + SERIES = {Adv. Lect. Math. (ALM)}, + VOLUME = {46}, + PAGES = {9--59}, + PUBLISHER = {Int. Press, Somerville, MA}, + YEAR = {[2019] \copyright 2019}, + MRCLASS = {14H37 (11G20 14H25)}, + MRNUMBER = {3971180}, +} + +@article {BCPS2017, + AUTHOR = {Bleher, Frauke M. and Chinburg, Ted and Poonen, Bjorn and + Symonds, Peter}, + TITLE = {Automorphisms of {H}arbater-{K}atz-{G}abber curves}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {368}, + YEAR = {2017}, + NUMBER = {1-2}, + PAGES = {811--836}, + ISSN = {0025-5831}, + MRCLASS = {14H37 (14G17 20F29)}, + MRNUMBER = {3651589}, + URL = {https://doi.org/10.1007/s00208-016-1490-2}, +} + +@article {Wiles, + AUTHOR = {Wiles, Andrew}, + TITLE = {Modular {E}lliptic {C}urves and {F}ermat's {L}ast {T}heorem}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {141}, + YEAR = {1995}, + NUMBER = {3}, + PAGES = {443--551}, + ISSN = {0003-486X}, + MRCLASS = {11G05 (11D41 11F11 11F80 11G18)}, + MRNUMBER = {1333035}, +MRREVIEWER = {Karl Rubin}, + URL = {https://doi.org/10.2307/2118559}, +} + +@book {FarbMagalit, + AUTHOR = {Farb, Benson and Margalit, Dan}, + TITLE = {A primer on mapping class groups}, + SERIES = {Princeton Mathematical Series}, + VOLUME = {49}, + PUBLISHER = {Princeton University Press, Princeton, NJ}, + YEAR = {2012}, + PAGES = {xiv+472}, + ISBN = {978-0-691-14794-9}, + MRCLASS = {57M50 (20F36 20F65 57M07 57N05)}, + MRNUMBER = {2850125}, +MRREVIEWER = {Stephen P. Humphries}, +} + +@book {BirmanBraids, + AUTHOR = {Birman, Joan S.}, + TITLE = {Braids, links, and mapping class groups}, + NOTE = {Annals of Mathematics Studies, No. 82}, + PUBLISHER = {Princeton University Press, Princeton, N.J.; University of + Tokyo Press, Tokyo}, + YEAR = {1974}, + PAGES = {ix+228}, + MRCLASS = {55A25}, + MRNUMBER = {0375281}, +MRREVIEWER = {Wilbur Whitten}, +} + + +@article{BCK, + journal = {Arxiv}, + title = {Galois structure of the holomorphic differential of curves }, + author = {Bleher, Frauke and Chinburg, Ted and Aristides, Kontogeorgis}, + file = {BCK.pdf}, + year = {2017}, + url = {https://arxiv.org/abs/1707.07133} +} + +@incollection {CaminaRachel, + AUTHOR = {Camina, Rachel}, + TITLE = {The {N}ottingham group}, + BOOKTITLE = {New horizons in pro-{$p$} groups}, + SERIES = {Progr. Math.}, + VOLUME = {184}, + PAGES = {205--221}, + PUBLISHER = {Birkh\"auser Boston, Boston, MA}, + YEAR = {2000}, + MRCLASS = {20E18}, + MRNUMBER = {1765121}, +MRREVIEWER = {Javier Otal}, +} + +@incollection {Deligne89, + AUTHOR = {Deligne, P.}, + TITLE = {Le groupe fondamental de la droite projective moins trois + points}, + BOOKTITLE = {Galois groups over {${\bf Q}$} ({B}erkeley, {CA}, 1987)}, + SERIES = {Math. Sci. Res. Inst. Publ.}, + VOLUME = {16}, + PAGES = {79--297}, + PUBLISHER = {Springer, New York}, + YEAR = {1989}, + MRCLASS = {14G25 (11G35 11M06 11R70 14F35 19E99 19F27)}, + MRNUMBER = {1012168}, +MRREVIEWER = {James Milne}, + URL = {https://doi.org/10.1007/978-1-4613-9649-9_3}, +} + +@book {bogoGrp, + AUTHOR = {Bogopolski, Oleg}, + TITLE = {Introduction to group theory}, + SERIES = {EMS Textbooks in Mathematics}, + NOTE = {Translated, revised and expanded from the 2002 Russian + original}, + PUBLISHER = {European Mathematical Society (EMS), Z\"urich}, + YEAR = {2008}, + PAGES = {x+177}, + ISBN = {978-3-03719-041-8}, + MRCLASS = {20-01 (20Dxx 20F28 20F65)}, + MRNUMBER = {2396717}, +MRREVIEWER = {Laurent Bartholdi}, + URL = {https://doi.org/10.4171/041}, +} + +@book {NeukirchBonn, + AUTHOR = {Neukirch, J\"urgen}, + TITLE = {Class {F}ield {T}heory}, + NOTE = {The Bonn lectures, edited and with a foreword by Alexander + Schmidt, + Translated from the 1967 German original by F. Lemmermeyer and + W. Snyder, + Language editor: A. Rosenschon}, + PUBLISHER = {Springer, Heidelberg}, + YEAR = {2013}, + PAGES = {xii+184}, + ISBN = {978-3-642-35436-6; 978-3-642-35437-3}, + MRCLASS = {11R37 (20J06)}, + MRNUMBER = {3058613}, + URL = {https://doi.org/10.1007/978-3-642-35437-3}, +} + +@book {KneserLGC, + AUTHOR = {Kneser, M.}, + TITLE = {Lectures on {G}alois cohomology of classical groups}, + NOTE = {With an appendix by T. A. Springer, + Notes by P. Jothilingam, + Tata Institute of Fundamental Research Lectures on + Mathematics, No. 47}, + PUBLISHER = {Tata Institute of Fundamental Research, Bombay}, + YEAR = {1969}, + PAGES = {ii+158}, + MRCLASS = {20G10 (12A60)}, + MRNUMBER = {0340440}, +MRREVIEWER = {R. Steinberg}, +} + +@article {Maclachlan, + AUTHOR = {Maclachlan, C.}, + TITLE = {Abelian groups of automorphisms of compact {R}iemann surfaces}, + JOURNAL = {Proc. London Math. Soc. (3)}, + FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, + VOLUME = {15}, + YEAR = {1965}, + PAGES = {699--712}, + ISSN = {0024-6115}, + MRCLASS = {30.45 (14.20)}, + MRNUMBER = {0179348}, +MRREVIEWER = {J. Mennicke}, + URL = {https://doi.org/10.1112/plms/s3-15.1.699}, +} + +@article {HyperadelicGamma, + AUTHOR = {Anderson, Greg W.}, + TITLE = {The hyperadelic gamma function}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {95}, + YEAR = {1989}, + NUMBER = {1}, + PAGES = {63--131}, + ISSN = {0020-9910}, + MRCLASS = {11S80 (11G20)}, + MRNUMBER = {969414}, +MRREVIEWER = {Gerd Faltings}, + URL = {https://doi.org/10.1007/BF01394145}, +} + + +@ARTICLE{Oda1985-qu, + title = "Note on meta-abelian quotients of pro-l free groups", + author = "Oda, T", + journal = "preprint", + year = 1985 +} + + +@book {antKonALGoem, + AUTHOR = {Αντωνιάδης, Ιωάννης Α. and Κοντογεώργης, Αριστείδης}, + TITLE = {Αλγεβρικές Καμπύλες, μια εισαγωγή στην Αλγεβρική Γεωμετρία}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Κάλλιπος}, + YEAR = {2021}, + PAGES = {iii+246}, + ISBN = {978-618-85370-1-9}, + URL = {https://www.dropbox.com/s/3u9kh0ujoi7zdyq/Kontogeorgis_master.pdf?dl=0}, +} + +@book {antkonAlgNTH, + AUTHOR = {Αντωνιάδης, Ιωάννης Α. and Κοντογεώργης, Αριστείδης}, + TITLE = {Αλγεβρική Θεωρία Αριθμών}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Κάλλιπος}, + YEAR = {2021}, + PAGES = {iii+311}, + ISBN = {978-618-85370-4-0}, + URL = {https://www.dropbox.com/s/ygy7ngyvzb5fyzf/Antoniadis_master.pdf?dl=0}, +} + + + +@book {antkonNT, + AUTHOR = {Αντωνιάδης, Ιωάννης Α. and Κοντογεώργης, Αριστείδης}, + TITLE = {Θεωρία Αριθμών και {Ε}φαρμογές}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Κάλλιπος}, + YEAR = {2015}, + PAGES = {ix+315}, + ISBN = {978-618-82124-5-9}, + URL = {https://eclass.uoa.gr/modules/document/file.php/MATH443/NumberTheoryNov2016.pdf}, +} + +@book {FiniteFields, + AUTHOR = {Αντωνιάδης, Ιωάννης Α. and Κοντογεώργης, Αριστείδης}, + TITLE = {Πεπερασμένα Σώματα και Κρυπτογραφία}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Κάλλιπος}, + YEAR = {2015}, + PAGES = {169}, + ISBN = {978-618-82124-6-6}, + URL = {https://eclass.uoa.gr/modules/document/file.php/MATH497/FiniteFieldsCrypto.pdf}, +} + +@book {StewartTall4, + AUTHOR = {Stewart, Ian and Tall, David}, + TITLE = {Algebraic {N}umber {T}heory and {F}ermat's {L}ast {T}heorem}, + EDITION = {4th edition}, + PUBLISHER = {CRC Press, Boca Raton, FL}, + YEAR = {2016}, + PAGES = {xix+322}, + ISBN = {978-1-4987-3839-2}, + MRCLASS = {11-01 (11D41 11Rxx)}, + MRNUMBER = {3443702}, +} + +@article {KontogBordeaux, + AUTHOR = {Kontogeorgis, Aristides}, + TITLE = {Field of moduli versus field of definition for cyclic covers + of the projective line}, + JOURNAL = {J. Th\'eor. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux}, + VOLUME = {21}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {679--692}, + ISSN = {1246-7405}, + MRCLASS = {14H37 (14H30)}, + MRNUMBER = {2605539}, +MRREVIEWER = {Meirav Topol-Amram}, + URL = {http://jtnb.cedram.org/item?id=JTNB_2009__21_3_679_0}, +} + +@book {KatoRigid, + AUTHOR = {Fujiwara, Kazuhiro and Kato Fumiharu}, + TITLE = {Foundations of Rigid Geometry I}, + PUBLISHER = {European Mathematical Society}, + YEAR = {2018}, + PAGES = {863}, + ISBN = {978-3-03719-135-4} +} + +@article {CrowellDerivedModule, + AUTHOR = {Crowell, R. H.}, + TITLE = {The derived module of a homomorphism}, + JOURNAL = {Advances in Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {6}, + YEAR = {1971}, + PAGES = {210--238 (1971)}, + ISSN = {0001-8708}, + MRCLASS = {20.10 (16.00)}, + MRNUMBER = {0276308}, +MRREVIEWER = {M. J. Dunwoody}, + URL = {https://doi.org/10.1016/0001-8708(71)90016-8}, +} + + +@book {RibesZalesskii, + AUTHOR = {Ribes, Luis and Zalesskii, Pavel}, + TITLE = {Profinite groups}, + SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A + Series of Modern Surveys in Mathematics [Results in + Mathematics and Related Areas. 3rd Series. A Series of Modern + Surveys in Mathematics]}, + VOLUME = {40}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2010}, + PAGES = {xvi+464}, + ISBN = {978-3-642-01641-7}, + MRCLASS = {20E18}, + MRNUMBER = {2599132}, + URL = {https://doi.org/10.1007/978-3-642-01642-4}, +} + +@MastersThesis{GPapas, + author = {Γεώργιος Παπάς}, + title = {Εισαγωγή στο πρόγραμμα {L}anglands}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2016}, + +} + +@MastersThesis{KontogeorgisFermat, + author = {Αριστείδης Κοντογεώργης}, + title = {Ημιευσταθείς Ελλειπτικές Καμπύλες και το τελευταίο θεώρημα του {F}ermat}, + school = {Πανεπιστήμιο Κρήτης}, + year = {1994}, + +} + +@MastersThesis{Hatzakos, + author = {Δημήτρης Χατζάκος}, + title = {Modular Forms και ελλειπτικές καμπύλες}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2012}, + +} + +@book{FrenkelEdward, +author = {Edward Frenkel}, +title = {Έρωτας και {Μ}αθηματικά}, +PUBLISHER ={Αλεξάνδρεια}, +pages = {328}, +ISBN ={9789602216675}, +year ={2015}, +} + +@book{SinghFermat, +author ={Singh Simon}, +title ={Το τελευταίο θεώρημα του {Φ}ερμά}, +publisher ={ Τραυλός, Αθήνα}, +series ={ Η γοητεία της γνώσης}, +year = {1998}, +pages = {400}, +isbn = {9789607122971}, +} + + + +@MastersThesis{KaranMsc, + author = {Σωτήρης Καρανικολόπουλος}, + title = {Uniformization Αλγεβρικών Καμπυλών}, + school = {Πανεπιστήμιο Αιγαίου}, + year = {2005}, +} + +@MastersThesis{TzortzakisMsc, + author = {Μανόλης Τζωρτζάκης}, + title = {Η θεωρία των dessin d’enfants του {G}rothendieck}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2014}, +} + +@MastersThesis{Tzortzakis, + author = {Μανόλης Τζωρτζάκης}, + title = {Η θεωρία των dessin d’enfants του {G}rothendieck}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2014}, +} + +@MastersThesis{AnthiZervou, + author = {Ανθή Ζερβού}, + title = { Profinite Groups and Cohomology}, + school = {Πανεπιστήμιο Κρήτης}, + year = {2017}, +} + +@MastersThesis{AnthiZervou2, + author = {Ανθή Ζερβού}, + title = {Πολυώνυμα και Θεωρία Galois}, + school = {Πανεπιστήμιο Κρήτης}, + year = {2015}, +} + +@book {FearlessSymmetry, + AUTHOR = {Ash, Avner and Gross, Robert}, + TITLE = {Fearless symmetry}, + NOTE = {Exposing the hidden patterns of numbers, + With a foreword by Barry Mazur}, + PUBLISHER = {Princeton University Press, Princeton, NJ}, + YEAR = {2006}, + PAGES = {xx+272}, + ISBN = {0-691-12492-2; 978-0-691-12492-6}, + MRCLASS = {11-01 (11D41 11F80 11G05)}, + MRNUMBER = {2229945}, +MRREVIEWER = {Lindsay N. Childs}, +} + +@misc{milneLECa, +author={Milne, James S.}, +title={Lectures on Etale Cohomology (v2.10)}, +year={2008}, +note={Available at www.jmilne.org/math/}, +pages={196} +} + +@MastersThesis{DimosAT, + author = {Δημοκλής Γκουνταρούλης}, + title = {Αριθμητική {Τ}οπολογία}, + school = {Πανεπιστήμιο Αιγαίου}, + year = {2006}, +} + +@MastersThesis{KardarisMsc, + author = {Δημήτρης Κάρδαρης}, + title = { Αριθμητική {Τ}οπολογία και {Φ}υσική}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2017}, +} + + +@ARTICLE{Kim_undated-cv, + title = {{Arithmetic {G}auge Theory: A Brief Introduction}}, + author = {Kim, Minhyong}, + url = {http://arxiv.org/abs/1712.07602v1}, + arxivid = {1712.07602v1}, + year = {2017}, +} + + +@ARTICLE{Wehrli2003-jj, + title = "Khovanov {H}omology and {C}onway {M}utation", + author = "Wehrli, Stephan M", + abstract = "We present an easy example of mutant links with different + Khovanov homology. The existence of such an example is + important because it shows that Khovanov homology cannot be + defined with a skein rule similar to the skein relation for + the Jones polynomial.", + month = jan, + year = 2003, + url = "http://arxiv.org/abs/math/0301312", + archivePrefix = "arXiv", + eprint = "math/0301312", + primaryClass = "math.GT", + arxivid = "math/0301312" +} + + +@ARTICLE{Turner2006-ck, + title = "Five {L}ectures on {K}hovanov {H}omology", + author = "Turner, Paul", + abstract = "These lecture notes, which were designed for the Summer + School ``Heegaard-Floer Homology and Khovanov Homology'' in + Marseilles, 29th May - 2nd June, 2006, provide an elementary + introduction to Khovanov homology. The intended audience is + graduate students with some minimal background in + low-dimensional and algebraic topology. The lectures cover + the basic definitions, important properties, a number of + variants and some applications. At the end of each lecture + the reader is referred to the relevant literature for + further reading.", + month = "19~" # jun, + year = 2006, + url = "http://arxiv.org/abs/math/0606464", + archivePrefix = "arXiv", + eprint = "math/0606464", + primaryClass = "math.GT", + arxivid = "math/0606464" +} + + +@ARTICLE{Kauffman2017-ra, + title = "New invariants of links and their state sum models", + author = "Kauffman, Louis H and Lambropoulou, Sofia", + abstract = "We introduce invariants of classical links, $H[R]$, $K[Q]$ + and $D[T]$, based on the invariants of knots, $R$, $Q$ and + $T$, denoting the regular isotopy version of the Homflypt + polynomial, the Kauffman polynomial and the Dubrovnik + polynomial. The invariants are obtained by abstracting the + skein relation of the corresponding invariant and making a + new skein algorithm comprising two computational levels: + first producing unlinked knotted components, then evaluating + the resulting knots. We provide skein theoretic proofs of + the well-definedness and topological properties of these + invariants. State sum models are formulated and + relationships with statistical mechanics models are + articulated. Finally, we discuss physical situations where + this course of action is taken naturally. The invariants in + this paper were revealed through generalizing the skein + theoretic definition of the invariants $\Theta_d$ related to + the Yokonuma--Hecke algebras and their 3-variable + generalization $\Theta$, which generalizes the Homflypt + polynomial as well as the linking number. $H[R]$ is the + regular isotopy counterpart of $\Theta$, so in this paper we + provide a direct skein-theoretic proof of the existence of + $\Theta$. The invariants $K[Q]$ and $D[T]$ are new + generalizations of the Kauffman and the Dubrovnik + polynomials.", + month = "10~" # mar, + year = 2017, + url = "http://arxiv.org/abs/1703.03655", + archivePrefix = "arXiv", + eprint = "1703.03655", + primaryClass = "math.GT", + arxivid = "1703.03655" +} + + +@ARTICLE{Lickorish1987-am, + title = "A polynomial invariant of oriented links", + author = "Lickorish, W B R and Millett, Kenneth C", + journal = "Topology", + volume = 26, + number = 1, + pages = "107--141", + year = 1987, + url = "http://www.sciencedirect.com/science/article/pii/0040938387900255", + issn = "0040-9383", + doi = "10.1016/0040-9383(87)90025-5" +} + +@article {JacobGFK, + AUTHOR = {Carvacho, Mariela and Hidalgo, Rub\'en A. and Quispe, Sa\'ul}, + TITLE = {Jacobian variety of generalized {F}ermat curves}, + JOURNAL = {Q. J. Math.}, + FJOURNAL = {The Quarterly Journal of Mathematics}, + VOLUME = {67}, + YEAR = {2016}, + NUMBER = {2}, + PAGES = {261--284}, + ISSN = {0033-5606}, + MRCLASS = {14H40 (14K02)}, + MRNUMBER = {3509993}, +MRREVIEWER = {Andreas H\"oring}, + URL = {https://doi.org/10.1093/qmath/haw009}, +} + + +@ARTICLE{holDifGFK, + title = "Holomorphic differentials of Generalized + {F}ermat curves", + author = "Hidalgo, Ruben A", + abstract = "For $k,n \geq 2$ integers, $(k-1)(n-1) >1$, let $F_\{k,n\}$ + be a generalized Fermat curve of type $(k,n)$, defined over + an algebraically closed field of characteristic $p \geq 0$ + (for $p>0$ we assume $k$ not divisible by $p$). We first + construct an explicit basis of its space + $H^\{1,0\}(F_\{k,n\})$ of holomorphic (regular) forms. For + $p=2$ (so $k \geq 3$ is odd), we describe the image of the + elements of that basis under the Cartier operator and we + obtain a lower bound for the dimension of its kernel, that + is, the space of its exact holomorphic forms. For $n=2,3$ + such a lower bound is sharp and for $n=4$ this is not the + case. In the case $p=3$, for the type $(2,4)$, we also + compute the exact holomorphic forms.", + journal = "arXiv [math.AG]", + month = oct, + year = 2017, + url = "https://arxiv.org/abs/1710.01349", + archivePrefix = "arXiv", + eprint = "1710.01349", + primaryClass = "math.AG", + arxivid = "1710.01349" +} + + +@article {LazardGradedLie, + AUTHOR = {Lazard, Michel}, + TITLE = {Sur les groupes nilpotents et les anneaux de {L}ie}, + JOURNAL = {Ann. Sci. Ecole Norm. Sup. (3)}, + FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Troisi\`eme + S\'erie}, + VOLUME = {71}, + YEAR = {1954}, + PAGES = {101--190}, + ISSN = {0012-9593}, + MRCLASS = {20.0X}, + MRNUMBER = {0088496}, +MRREVIEWER = {B. H. Neumann}, + URL = {http://www.numdam.org/item?id=ASENS_1954_3_71_2_101_0}, +} + +@book {Gould72, + AUTHOR = {Gould, Henry W.}, + TITLE = {Combinatorial identities}, + NOTE = {A standardized set of tables listing 500 binomial coefficient + summations}, + PUBLISHER = {Henry W. Gould, Morgantown, W.Va.}, + YEAR = {1972}, + PAGES = {viii+106}, + MRCLASS = {05A19 (65A05)}, + MRNUMBER = {0354401}, +} + +@book {CampbellWehlauModular, + AUTHOR = {Campbell, H. E. A. Eddy and Wehlau, David L.}, + TITLE = {Modular invariant theory}, + SERIES = {Encyclopaedia of Mathematical Sciences}, + VOLUME = {139}, + NOTE = {Invariant Theory and Algebraic Transformation Groups, 8}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2011}, + PAGES = {xiv+233}, + ISBN = {978-3-642-17403-2}, + MRCLASS = {13A50 (13E15 20F29)}, + MRNUMBER = {2759466}, +MRREVIEWER = {Frank D. Grosshans}, + DOI = {10.1007/978-3-642-17404-9}, + URL = {https://doi.org/10.1007/978-3-642-17404-9}, +} + + +@book {SmithPolInv, + AUTHOR = {Smith, Larry}, + TITLE = {Polynomial invariants of finite groups}, + SERIES = {Research Notes in Mathematics}, + VOLUME = {6}, + PUBLISHER = {A K Peters, Ltd., Wellesley, MA}, + YEAR = {1995}, + PAGES = {xvi+360}, + ISBN = {1-56881-053-9}, + MRCLASS = {13A50 (20-01 55S10)}, + MRNUMBER = {1328644}, +MRREVIEWER = {Frank D. Grosshans}, +} + + +@book {BensonPolInv, + AUTHOR = {Benson, D. J.}, + TITLE = {Polynomial invariants of finite groups}, + SERIES = {London Mathematical Society Lecture Note Series}, + VOLUME = {190}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1993}, + PAGES = {x+118}, + ISBN = {0-521-45886-2}, + MRCLASS = {13A50 (13E15 20F29)}, + MRNUMBER = {1249931}, +MRREVIEWER = {Frank D. Grosshans}, + DOI = {10.1017/CBO9780511565809}, + URL = {https://doi.org/10.1017/CBO9780511565809}, +} + + +@book {MumfordAbelian, + AUTHOR = {Mumford, David}, + TITLE = {Abelian varieties}, + SERIES = {Tata Institute of Fundamental Research Studies in Mathematics}, + VOLUME = {5}, + NOTE = {With appendices by C. P. Ramanujam and Yuri Manin, + Corrected reprint of the second (1974) edition}, + PUBLISHER = {Published for the Tata Institute of Fundamental Research, + Bombay; by Hindustan Book Agency, New Delhi}, + YEAR = {2008}, + PAGES = {xii+263}, + ISBN = {978-81-85931-86-9; 81-85931-86-0}, + MRCLASS = {14Kxx}, + MRNUMBER = {2514037}, +} + +@misc{stacks-project, + shorthand = {Stacks}, + author = {The {Stacks Project Authors}}, + title = {\textit{Stacks Project}}, + howpublished = {\url{http://stacks.math.columbia.edu}}, + year = {2018}, +} + + + +@article {GlasbyPraegesCherylXia, + AUTHOR = {Glasby, S. P. and Praeger, Cheryl E. and Xia, Binzhou}, + TITLE = {Decomposing modular tensor products, and periodicity of + `{J}ordan partitions'}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {450}, + YEAR = {2016}, + PAGES = {570--587}, + ISSN = {0021-8693}, + MRCLASS = {15A69 (15A21)}, + MRNUMBER = {3449704}, +MRREVIEWER = {Haifeng Ma}, + DOI = {10.1016/j.jalgebra.2015.11.025}, + URL = {https://doi.org/10.1016/j.jalgebra.2015.11.025}, +} + +@book {K-theorySwan, + AUTHOR = {Swan, Richard G.}, + TITLE = {{$K$}-theory of finite groups and orders}, + SERIES = {Lecture Notes in Mathematics, Vol. 149}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1970}, + PAGES = {iv+237}, + MRCLASS = {16A54 (18F25)}, + MRNUMBER = {0308195}, +MRREVIEWER = {H. Bass}, +} + + +@book {BensonElAb, + AUTHOR = {Benson, David J.}, + TITLE = {Representations of elementary abelian {$p$}-groups and vector + bundles}, + SERIES = {Cambridge Tracts in Mathematics}, + VOLUME = {208}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2017}, + PAGES = {xvii+328}, + ISBN = {978-1-107-17417-7}, + MRCLASS = {20C20 (14J60 14L30)}, + MRNUMBER = {3585474}, +MRREVIEWER = {Alan Koch}, + DOI = {10.1017/9781316795699}, + URL = {https://doi.org/10.1017/9781316795699}, +} + + + +@article {MR1843324, + AUTHOR = {Hughes, Ian and Kemper, Gregor}, + TITLE = {Symmetric powers of modular representations for groups with a + {S}ylow subgroup of prime order}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {241}, + YEAR = {2001}, + NUMBER = {2}, + PAGES = {759--788}, + ISSN = {0021-8693}, + MRCLASS = {13A50 (13D40 20C20)}, + MRNUMBER = {1843324}, +MRREVIEWER = {Anne Elisabeth Henke}, + DOI = {10.1006/jabr.2000.8710}, + URL = {https://doi.org/10.1006/jabr.2000.8710}, +} + + +@article {MR1747371, + AUTHOR = {Hughes, Ian and Kemper, Gregor}, + TITLE = {Symmetric powers of modular representations, {H}ilbert series + and degree bounds}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {28}, + YEAR = {2000}, + NUMBER = {4}, + PAGES = {2059--2088}, + ISSN = {0092-7872}, + MRCLASS = {13A50 (13D40)}, + MRNUMBER = {1747371}, +MRREVIEWER = {Dmitri I. Panyushev}, + DOI = {10.1080/00927870008826944}, + URL = {https://doi.org/10.1080/00927870008826944}, +} + +@article {MR2323446, + AUTHOR = {Symonds, Peter}, + TITLE = {Cyclic group actions on polynomial rings}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {39}, + YEAR = {2007}, + NUMBER = {2}, + PAGES = {181--188}, + ISSN = {0024-6093}, + MRCLASS = {20C15 (13D02)}, + MRNUMBER = {2323446}, + DOI = {10.1112/blms/bdl023}, + URL = {https://doi.org/10.1112/blms/bdl023}, +} + +@incollection {MR499459, + AUTHOR = {Almkvist, Gert and Fossum, Robert}, + TITLE = {Decomposition of exterior and symmetric powers of + indecomposable {${\bf Z}/p{\bf Z}$}-modules in characteristic + {$p$}\ and relations to invariants}, + BOOKTITLE = {S\'eminaire d'{A}lg\`ebre {P}aul {D}ubreil, 30\`eme ann\'ee ({P}aris, + 1976--1977)}, + SERIES = {Lecture Notes in Math.}, + VOLUME = {641}, + PAGES = {1--111}, + PUBLISHER = {Springer, Berlin}, + YEAR = {1978}, + MRCLASS = {14L30 (13H10 16A26 20C05)}, + MRNUMBER = {499459}, +MRREVIEWER = {H. R\"ohrl}, +} + + +@article {MR0144980, + AUTHOR = {Heller, A. and Reiner, I.}, + TITLE = {Representations of cyclic groups in rings of integers. {II}}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {77}, + YEAR = {1963}, + PAGES = {318--328}, + ISSN = {0003-486X}, + MRCLASS = {20.80}, + MRNUMBER = {0144980}, +MRREVIEWER = {Rimhak Ree}, + DOI = {10.2307/1970218}, + URL = {https://doi.org/10.2307/1970218}, +} + + +@article {MR0140575, + AUTHOR = {Heller, A. and Reiner, I.}, + TITLE = {Representations of cyclic groups in rings of integers. {I}}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {76}, + YEAR = {1962}, + PAGES = {73--92}, + ISSN = {0003-486X}, + MRCLASS = {20.80}, + MRNUMBER = {0140575}, +MRREVIEWER = {Rimhak Ree}, + DOI = {10.2307/1970266}, + URL = {https://doi.org/10.2307/1970266}, +} + +@article {MR0002133, + AUTHOR = {Diederichsen, Fritz-Erdmann}, + TITLE = {\"{U}ber die {A}usreduktion ganzzahliger {G}ruppendarstellungen + bei arithmetischer \"{A}quivalenz}, + JOURNAL = {Abh. Math. Sem. Hansischen Univ.}, + VOLUME = {13}, + YEAR = {1940}, + PAGES = {357--412}, + MRCLASS = {20.0X}, + MRNUMBER = {0002133}, +MRREVIEWER = {R. Brauer}, +} + + + +@ARTICLE{Gudivok1992-zp, + title = "Representations of finite p-groups over the ring of formal power + series with integral p-adic coefficients", + author = "Gudivok, P M and Oros, V M and Roiter, A V", + abstract = "A classification is given of the representations of the cyclic + group of order p over the ringℤ p [[x]] of formal power series + with integral p-adic coefficients and it is proved that in the + other cases the problem of representations of a finite, p-group + overℤ P [[x1,...xn]] is wild.", + journal = "Ukrainian Math. J.", + volume = 44, + number = 6, + pages = "678--689", + month = jun, + year = 1992, + url = "https://doi.org/10.1007/BF01056947", + issn = "0041-5995, 1573-9376", + doi = "10.1007/BF01056947" +} + +@article {MR634458, + AUTHOR = {B\'ayer, Pilar and Neukirch, J\"urgen}, + TITLE = {On automorphic forms and {H}odge theory}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {257}, + YEAR = {1981}, + NUMBER = {2}, + PAGES = {137--155}, + ISSN = {0025-5831}, + MRCLASS = {10D15 (10D45 14C30 14F40)}, + MRNUMBER = {634458}, +MRREVIEWER = {Steven M. Zucker}, + DOI = {10.1007/BF01458280}, + URL = {https://doi.org/10.1007/BF01458280}, +} + +@article {KlopschAut, + AUTHOR = {Klopsch, Benjamin}, + TITLE = {Automorphisms of the {N}ottingham group}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {223}, + YEAR = {2000}, + NUMBER = {1}, + PAGES = {37--56}, + ISSN = {0021-8693}, + MRCLASS = {20E18 (20F28)}, + MRNUMBER = {1738250}, +MRREVIEWER = {Andrea Caranti}, + DOI = {10.1006/jabr.1999.8040}, + URL = {https://doi.org/10.1006/jabr.1999.8040}, +} + +@article {LubinTorsionNottingham, + AUTHOR = {Lubin, Jonathan}, + TITLE = {Torsion in the {N}ottingham group}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {43}, + YEAR = {2011}, + NUMBER = {3}, + PAGES = {547--560}, + ISSN = {0024-6093}, + MRCLASS = {11S31 (20E18 37P35)}, + MRNUMBER = {2820144}, +MRREVIEWER = {Benjamin Klopsch}, + DOI = {10.1112/blms/bdq120}, + URL = {https://doi.org/10.1112/blms/bdq120}, +} + +@article {BleherChinburgPoonenSymondsAutHKG, + AUTHOR = {Bleher, Frauke M. and Chinburg, Ted and Poonen, Bjorn and + Symonds, Peter}, + TITLE = {Automorphisms of {H}arbater-{K}atz-{G}abber curves}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {368}, + YEAR = {2017}, + NUMBER = {1-2}, + PAGES = {811--836}, + ISSN = {0025-5831}, + MRCLASS = {14H37 (14G17 20F29)}, + MRNUMBER = {3651589}, + DOI = {10.1007/s00208-016-1490-2}, + URL = {https://doi.org/10.1007/s00208-016-1490-2}, +} + +@article {MR3651589, + AUTHOR = {Bleher, Frauke M. and Chinburg, Ted and Poonen, Bjorn and + Symonds, Peter}, + TITLE = {Automorphisms of {H}arbater-{K}atz-{G}abber curves}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {368}, + YEAR = {2017}, + NUMBER = {1-2}, + PAGES = {811--836}, + ISSN = {0025-5831}, + MRCLASS = {14H37 (14G17 20F29)}, + MRNUMBER = {3651589}, +MRREVIEWER = {Aristides I. Kontogeorgis}, + DOI = {10.1007/s00208-016-1490-2}, + URL = {https://doi.org/10.1007/s00208-016-1490-2}, +} + + +@book {GroebnerAdams, + AUTHOR = {Adams, William W. and Loustaunau, Philippe}, + TITLE = {An introduction to {G}r\"obner bases}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {3}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1994}, + PAGES = {xiv+289}, + ISBN = {0-8218-3804-0}, + MRCLASS = {13P10 (13-01 68Q40)}, + MRNUMBER = {1287608}, +MRREVIEWER = {Joachim Apel}, + DOI = {10.1090/gsm/003}, + URL = {https://doi.org/10.1090/gsm/003}, +} + +@book {FadeevQuantum, + AUTHOR = {Faddeev, L. D. and Yakubovski\u\i , O. A.}, + TITLE = {Lectures on quantum mechanics for mathematics students}, + SERIES = {Student Mathematical Library}, + VOLUME = {47}, + NOTE = {Translated from the 1980 Russian original by Harold McFaden, + With an appendix by Leon Takhtajan}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2009}, + PAGES = {xii+234}, + ISBN = {978-0-8218-4699-5}, + MRCLASS = {81-01 (81Q10 81R05 81S30)}, + MRNUMBER = {2492178}, +MRREVIEWER = {Howard E. Brandt}, + DOI = {10.1090/stml/047}, + URL = {https://doi.org/10.1090/stml/047}, +} + +@mastersthesis{Tatsis, + author = {Γ. Τάτσης}, + title = {{$\Lambda$}-δακτύλιοι και το σώμα με ένα στοιχείο}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2017}, + +} + +@article {Wade43, + AUTHOR = {Wade, L. I.}, + TITLE = {Certain quantities transcendental over {$GF(p^n,x)$}. {II}}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {10}, + YEAR = {1943}, + PAGES = {587--594}, + ISSN = {0012-7094}, + MRCLASS = {09.1X}, + MRNUMBER = {0009023}, +MRREVIEWER = {J. L. Dorroh}, + URL = {http://projecteuclid.org/euclid.dmj/1077472105}, +} + + +@book{AntoniadisANTH, +AUTHOR = {Αντωνιάδης, Ιωάννης Α.}, + TITLE = {Αλγεβρική Θεωρία Αριθμών}, + publisher = {Διδακτικές σημειώσεις, {Π}ανεπιστήμιο Κρήτης}, + year ={1986} +} + +@book{ΑntoniadisHis, +AUTHOR = {Αντωνιάδης, Ιωάννης Α.}, + TITLE = {Θεωρία Αριθµών κατά τον 17ο και 18ο αιώνα}, + publisher = {Ηράκλειο: {Π}ανεπιστήμιο Κρήτης}, + year ={1999} +} + +@book{ΑntoniadisL, +AUTHOR = {Αντωνιάδης, Ιωάννης Α. }, + TITLE = {L-σειρές}, + publisher = {Ηράκλειο: {Π}ανεπιστήμιο Κρήτης}, + year ={1999} +} + +@book{ΑntoniadisEC, +AUTHOR = {Αντωνιάδης, Ιωάννης Α. }, + TITLE = {Ελλειπτικές Καμπύλες}, + publisher = {Ηράκλειο: {Π}ανεπιστήμιο Κρήτης}, + year ={1999} +} + +@book{AntoniadisParas, +AUTHOR = {Αντωνιάδης, Ιωάννης Α. }, + TITLE = {Θεωρία Παραστάσεων πεπερασμένων ομάδων}, + publisher = {Ηράκλειο: {Π}ανεπιστήμιο Κρήτης}, + year ={1996} +} + +@incollection {MR1638478, + AUTHOR = {Tate, John}, + TITLE = {Finite flat group schemes}, + BOOKTITLE = {Modular forms and {F}ermat's last theorem ({B}oston, {MA}, + 1995)}, + PAGES = {121--154}, + PUBLISHER = {Springer, New York}, + YEAR = {1997}, + MRCLASS = {14L15}, + MRNUMBER = {1638478}, +} + +@book {MR1885791, + AUTHOR = {Hasse, Helmut}, + TITLE = {Number {T}heory}, + SERIES = {Classics in Mathematics}, + EDITION = {German}, + NOTE = {Reprint of the 1980 English edition [Springer, Berlin; + MR0562104 (81c:12001b)], + Edited and with a preface by Horst G\"unter Zimmer}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2002}, + PAGES = {xviii+638}, + ISBN = {3-540-42749-X}, + MRCLASS = {11-01 (01A75 11Rxx)}, + MRNUMBER = {1885791}, +} + +@book {MR1376367, + AUTHOR = {Lorenzini, Dino}, + TITLE = {An invitation to arithmetic geometry}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {9}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1996}, + PAGES = {xvi+397}, + ISBN = {0-8218-0267-4}, + MRCLASS = {14G40 (11G20 14-01)}, + MRNUMBER = {1376367}, +MRREVIEWER = {I. Dolgachev}, + DOI = {10.1090/gsm/009}, + URL = {https://doi.org/10.1090/gsm/009}, +} + +@article {EMEKontogeorgis, + AUTHOR = {Αντωνιάδης, Ιωάννης Α. and Κοντογεώργης, Αριστείδης}, + TITLE = {Αριθμητική Γεωμετρία, Ιστορία, Επιτεύγματα και μέλλον}, + JOURNAL = {Τόμος της Ελληνικής Μαθηματικής Εταιρείας για τα 100 χρόνια από την ίδρυσή της}, + YEAR = {2018} +} + +@article {MR0384707, + AUTHOR = {Drinfel\cprime d, V. G.}, + TITLE = {Elliptic modules}, + JOURNAL = {Mat. Sb. (N.S.)}, + VOLUME = {94(136)}, + YEAR = {1974}, + PAGES = {594--627, 656}, + MRCLASS = {10D99 (14K15)}, + MRNUMBER = {0384707}, +MRREVIEWER = {Pierre Deligne}, +} + +@article {MR1506871, + AUTHOR = {Carlitz, Leonard}, + TITLE = {The {A}rithmetic of {P}olynomials in a {G}alois {F}ield}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {54}, + YEAR = {1932}, + NUMBER = {1}, + PAGES = {39--50}, + ISSN = {0002-9327}, + MRCLASS = {DML}, + MRNUMBER = {1506871}, + DOI = {10.2307/2371075}, + URL = {https://doi.org/10.2307/2371075}, +} + +@incollection {MR535766, + AUTHOR = {Hayes, David R.}, + TITLE = {Explicit class field theory in global function fields}, + BOOKTITLE = {Studies in algebra and number theory}, + SERIES = {Adv. in Math. Suppl. Stud.}, + VOLUME = {6}, + PAGES = {173--217}, + PUBLISHER = {Academic Press, New York-London}, + YEAR = {1979}, + MRCLASS = {12A90 (10D30 12A65)}, + MRNUMBER = {535766}, +MRREVIEWER = {W.-D. Geyer}, +} + +@article {MR0330106, + AUTHOR = {Hayes, D. R.}, + TITLE = {Explicit class field theory for rational function fields}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {189}, + YEAR = {1974}, + PAGES = {77--91}, + ISSN = {0002-9947}, + MRCLASS = {12A65 (12A90)}, + MRNUMBER = {0330106}, +MRREVIEWER = {Bostwick F. Wyman}, + DOI = {10.2307/1996848}, + URL = {https://doi.org/10.2307/1996848}, +} + +@book {MR1876657, + AUTHOR = {Rosen, Michael}, + TITLE = {Number theory in function fields}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {210}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2002}, + PAGES = {xii+358}, + ISBN = {0-387-95335-3}, + MRCLASS = {11R58 (11R60 11T55)}, + MRNUMBER = {1876657}, +MRREVIEWER = {Ernst-Ulrich Gekeler}, + DOI = {10.1007/978-1-4757-6046-0}, + URL = {https://doi.org/10.1007/978-1-4757-6046-0}, +} + +@book {MR2241963, + AUTHOR = {Villa Salvador, Gabriel Daniel}, + TITLE = {Topics in the theory of algebraic function fields}, + SERIES = {Mathematics: Theory \& Applications}, + PUBLISHER = {Birkh\"auser Boston, Inc., Boston, MA}, + YEAR = {2006}, + PAGES = {xviii+652}, + ISBN = {978-0-8176-4480-2; 0-8176-4480-6}, + MRCLASS = {11-02 (11R32 11R58 11S20 94A60)}, + MRNUMBER = {2241963}, +MRREVIEWER = {Manfred Lochter}, +} + +@book {MR1231797, + AUTHOR = {Murty, V. Kumar}, + TITLE = {Introduction to abelian varieties}, + SERIES = {CRM Monograph Series}, + VOLUME = {3}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1993}, + PAGES = {xiv+112}, + ISBN = {0-8218-6995-7}, + MRCLASS = {14Kxx (11G10 14-00 14K05)}, + MRNUMBER = {1231797}, +MRREVIEWER = {H. Lange}, +} + +@article {MR0074086, + AUTHOR = {Hirzebruch, Friedrich}, + TITLE = {Arithmetic genera and the theorem of {R}iemann-{R}och for + algebraic varieties}, + JOURNAL = {Proc. Nat. Acad. Sci. U. S. A.}, + FJOURNAL = {Proceedings of the National Academy of Sciences of the United + States of America}, + VOLUME = {40}, + YEAR = {1954}, + PAGES = {110--114}, + ISSN = {0027-8424}, + MRCLASS = {14.0X}, + MRNUMBER = {0074086}, +MRREVIEWER = {B. Eckmann}, +} + +@book {MR1644323, + AUTHOR = {Fulton, William}, + TITLE = {Intersection theory}, + SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A + Series of Modern Surveys in Mathematics [Results in + Mathematics and Related Areas. 3rd Series. A Series of Modern + Surveys in Mathematics]}, + VOLUME = {2}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1998}, + PAGES = {xiv+470}, + ISBN = {3-540-62046-X; 0-387-98549-2}, + MRCLASS = {14C17 (14-02)}, + MRNUMBER = {1644323}, + DOI = {10.1007/978-1-4612-1700-8}, + URL = {https://doi.org/10.1007/978-1-4612-1700-8}, +} + +@article {MR740897, + AUTHOR = {Faltings, Gerd}, + TITLE = {Calculus on arithmetic surfaces}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {119}, + YEAR = {1984}, + NUMBER = {2}, + PAGES = {387--424}, + ISSN = {0003-486X}, + MRCLASS = {14H25 (14G99)}, + MRNUMBER = {740897}, +MRREVIEWER = {G. van der Geer}, + DOI = {10.2307/2007043}, + URL = {https://doi.org/10.2307/2007043}, +} + +@article {MR0466150, + AUTHOR = {Arakelov, S. J.}, + TITLE = {Theory of intersections on the arithmetic surface}, + BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of + {M}athematicians ({V}ancouver, {B}.{C}., 1974), {V}ol. 1}, + PAGES = {405--408}, + PUBLISHER = {Canad. Math. Congress, Montreal, Que.}, + YEAR = {1975}, + MRCLASS = {14J20 (14C10)}, + MRNUMBER = {0466150}, +} + +@article {MR0472815, + AUTHOR = {Arakelov, S. Ju.}, + TITLE = {An intersection theory for divisors on an arithmetic surface}, + JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.}, + FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, + VOLUME = {38}, + YEAR = {1974}, + PAGES = {1179--1192}, + ISSN = {0373-2436}, + MRCLASS = {14C15}, + MRNUMBER = {0472815}, +MRREVIEWER = {Gerhard Pfister}, +} + +@misc{GRR, + author = {Patrick J.R. Ryan}, + title = {The {G}rothendieck-{R}iemann-{R}och Theorem}, + school = {Harvard University}, + year = {2015}, + note = {προπτυχιακή εργασία} +} + + + + + +@misc{GRR-rigoroustrivialities, + title = {The {C}how Ring and {C}hern Classes}, + author= {Matt DeLand}, + howpublished = {https://rigtriv.wordpress.com/2009/03/22/the-chow-ring-and-chern-classes/}, + note = {Accessed: 31-8-2018} +} + +@book {MR1406314, + AUTHOR = {Beauville, Arnaud}, + TITLE = {Complex algebraic surfaces}, + SERIES = {London Mathematical Society Student Texts}, + VOLUME = {34}, + EDITION = {Second}, + NOTE = {Translated from the 1978 French original by R. Barlow, with + assistance from N. I. Shepherd-Barron and M. Reid}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1996}, + PAGES = {x+132}, + ISBN = {0-521-49510-5; 0-521-49842-2}, + MRCLASS = {14Jxx (14-02)}, + MRNUMBER = {1406314}, + DOI = {10.1017/CBO9780511623936}, + URL = {https://doi.org/10.1017/CBO9780511623936}, +} + +@article {MR0116022, + AUTHOR = {Borel, Armand and Serre, Jean-Pierre}, + TITLE = {Le th\'eor\`eme de {R}iemann-{R}och}, + JOURNAL = {Bull. Soc. Math. France}, + FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France}, + VOLUME = {86}, + YEAR = {1958}, + PAGES = {97--136}, + ISSN = {0037-9484}, + MRCLASS = {14.00}, + MRNUMBER = {0116022}, +MRREVIEWER = {R. Bott}, + URL = {http://www.numdam.org/item?id=BSMF_1958__86__97_0}, +} + +@book {MR2514094, + AUTHOR = {Silverman, Joseph H.}, + TITLE = {The arithmetic of elliptic curves}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {106}, + EDITION = {Second}, + PUBLISHER = {Springer, Dordrecht}, + YEAR = {2009}, + PAGES = {xx+513}, + ISBN = {978-0-387-09493-9}, + MRCLASS = {11-02 (11G05 11G20 14H52 14K15)}, + MRNUMBER = {2514094}, +MRREVIEWER = {Vasil\cprime \={I}. Andr\={i}\u{i}chuk}, + DOI = {10.1007/978-0-387-09494-6}, + URL = {https://doi.org/10.1007/978-0-387-09494-6}, +} + +@book {MR0419430, + AUTHOR = {Mumford, David}, + TITLE = {Curves and their {J}acobians}, + PUBLISHER = {The University of Michigan Press, Ann Arbor, Mich.}, + YEAR = {1975}, + PAGES = {vi+104}, + MRCLASS = {14-01 (14HXX)}, + MRNUMBER = {0419430}, +MRREVIEWER = {Henry C. Pinkham}, +} + +@article {MR0206004, + AUTHOR = {Tate, John}, + TITLE = {Endomorphisms of abelian varieties over finite fields}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {2}, + YEAR = {1966}, + PAGES = {134--144}, + ISSN = {0020-9910}, + MRCLASS = {14.51 (14.40)}, + MRNUMBER = {0206004}, +MRREVIEWER = {O. F. G. Schilling}, + DOI = {10.1007/BF01404549}, + URL = {https://doi.org/10.1007/BF01404549}, +} + + + +@ARTICLE{Kontogeorgis2018-py, + title = "Actions on Symmetric curves from the Arithmetic Topology + viewpoint", + author = "Kontogeorgis, Aristides and Paramantzoglou, Panagiotis", + abstract = "We give an explanation of the MKR dictionary in Arithmetic + topology using Ihara's theory of profinite braid groups. + Motivated by the analogy we perform explicit computations + for representations of both braid groups and the absolute + Galois group $\mathrm\{Gal\}(\bar\{\Q\}/\Q)$ for cyclic + covers of the projective line and generalized Fermat curves.", + month = apr, + year = 2018, + url = "http://arxiv.org/abs/1804.07021", + archivePrefix = "arXiv", + eprint = "1804.07021", + primaryClass = "math.NT", + arxivid = "1804.07021" +} + +@book {MR1711577, + AUTHOR = {Malle, Gunter and Matzat, B. Heinrich}, + TITLE = {Inverse {G}alois theory}, + SERIES = {Springer Monographs in Mathematics}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1999}, + PAGES = {xvi+436}, + ISBN = {3-540-62890-8}, + MRCLASS = {12F12 (11R32 12F10 14G32 20C33 20F36 20G40)}, + MRNUMBER = {1711577}, +MRREVIEWER = {Helmut V\"{o}lklein}, + DOI = {10.1007/978-3-662-12123-8}, + URL = {https://doi.org/10.1007/978-3-662-12123-8}, +} + +@book {MR1812024, + AUTHOR = {Lyndon, Roger C. and Schupp, Paul E.}, + TITLE = {Combinatorial group theory}, + SERIES = {Classics in Mathematics}, + NOTE = {Reprint of the 1977 edition}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2001}, + PAGES = {xiv+339}, + ISBN = {3-540-41158-5}, + MRCLASS = {20Fxx (20Exx 57M07)}, + MRNUMBER = {1812024}, + DOI = {10.1007/978-3-642-61896-3}, + URL = {https://doi.org/10.1007/978-3-642-61896-3}, +} + + +@article {AiJu1, + AUTHOR = {Aicardi, Francesca and Juyumaya, Jes\'{u}s}, + TITLE = {Markov trace on the algebra of braids and ties}, + JOURNAL = {Mosc. Math. J.}, + FJOURNAL = {Moscow Mathematical Journal}, + VOLUME = {16}, + YEAR = {2016}, + NUMBER = {3}, + PAGES = {397--431}, + ISSN = {1609-3321}, + MRCLASS = {57M27 (20C08 20F36 57M25)}, + MRNUMBER = {3510208}, +MRREVIEWER = {Ioannis Diamantis}, +} + +@article {AiJu2, + AUTHOR = {Aicardi, Francesca and Juyumaya, Jes\'{u}s}, + TITLE = {Tied links}, + JOURNAL = {J. Knot Theory Ramifications}, + FJOURNAL = {Journal of Knot Theory and its Ramifications}, + VOLUME = {25}, + YEAR = {2016}, + NUMBER = {9}, + PAGES = {1641001, 28}, + ISSN = {0218-2165}, + MRCLASS = {57M25 (20C08 20F36)}, + MRNUMBER = {3544429}, +MRREVIEWER = {Ioannis Diamantis}, + DOI = {10.1142/S0218216516410017}, + URL = {https://doi.org/10.1142/S0218216516410017}, +} + + +@ARTICLE{CJKL, + title = "Identifying the Invariants for Classical Knots and Links from the + {Yokonuma--Hecke} Algebras", + author = "Chlouveraki, Maria and Juyumaya, Jes{\'u}s and Karvounis, + Konstantinos and Lambropoulou, Sofia", + abstract = "We announce the existence of a family of new 2-variable + polynomial invariants for oriented classical links defined via a + Markov trace on the Yokonuma--Hecke algebra of type A. + Yokonuma--Hecke algebras are generalizations of Iwahori--Hecke + algebras, and this family contains the HOMFLYPT polynomial, the + famous 2-variable invariant for classical links arising from the + Iwahori--Hecke algebra of type A. We show that these invariants + are topologically equivalent to the HOMFLYPT polynomial on knots, + but not on links, by providing pairs of HOMFLYPT-equivalent links + that are distinguished by our invariants. In order to do this, we + prove that our invariants can be defined diagrammatically via a + special skein relation involving only crossings between different + components. We further generalize this family of invariants to a + new 3-variable skein link invariant that is stronger than the + HOMFLYPT polynomial. Finally, we present a closed formula for + this invariant, by W. B. R. Lickorish, that uses HOMFLYPT + polynomials of sublinks and linking numbers of a given oriented + link.", + journal = "Int. Mathem. Res. Not.", + month = mar, + year = 2018, + url = "https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rny013/4938565?redirectedFrom=fulltext", + issn = "1073-7928", + doi = "10.1093/imrn/rny013" +} + +@article {GJKL, + AUTHOR = {Goundaroulis, Dimos and Juyumaya, Jes\'{u}s and Kontogeorgis, + Aristides and Lambropoulou, Sofia}, + TITLE = {Framization of the {T}emperley-{L}ieb algebra}, + JOURNAL = {Math. Res. Lett.}, + FJOURNAL = {Mathematical Research Letters}, + VOLUME = {24}, + YEAR = {2017}, + NUMBER = {2}, + PAGES = {299--345}, + ISSN = {1073-2780}, + MRCLASS = {57M27 (20C08 20F36 57M25)}, + MRNUMBER = {3685273}, +MRREVIEWER = {Ioannis Diamantis}, + DOI = {10.4310/MRL.2017.v24.n2.a3}, + URL = {https://doi.org/10.4310/MRL.2017.v24.n2.a3}, +} + + +@ARTICLE{GoLa, + title = "A new two-variable generalization of the Jones polynomial", + author = "Goundaroulis, Dimos and Lambropoulou, Sofia", + abstract = "We present a new 2-variable generalization of the Jones + polynomial that can be defined through the skein relation of + the Jones polynomial. The well-definedness of this new + generalization is proved both algebraically and + diagrammatically as well as via a closed combinatorial + formula. This new invariant is able to distinguish more + pairs of non-isotopic links than the original Jones + polynomial such as the Thistlethwaite link from the unlink + with two components.", + month = aug, + year = 2016, + url = "http://arxiv.org/abs/1608.01812", + archivePrefix = "arXiv", + eprint = "1608.01812", + primaryClass = "math.GT", + arxivid = "1608.01812" +} + + +@book {CGKL1, +AUTHOR = {Chlouveraki, M. and Goundaroulis, D. and Kontogeorgis, A. and Lambropoulou, S.}, + TITLE = {A skein ralation for Khovanov Homology and a Categorification of the $\theta$-invariant}, + SERIES = {}, + NOTE = {In preparation}, + PUBLISHER = {}, + ADDRESS = {}, + YEAR = {}, + PAGES = {220}, + ISBN = {}, + MRCLASS = {}, + MRNUMBER = {}, +MRREVIEWER = {}, +} + +@article {MR1740682, + AUTHOR = {Khovanov, Mikhail}, + TITLE = {A categorification of the {J}ones polynomial}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {101}, + YEAR = {2000}, + NUMBER = {3}, + PAGES = {359--426}, + ISSN = {0012-7094}, + MRCLASS = {57M27 (57R56)}, + MRNUMBER = {1740682}, + DOI = {10.1215/S0012-7094-00-10131-7}, + URL = {https://doi.org/10.1215/S0012-7094-00-10131-7}, +} + + +@article {MR3591155, + AUTHOR = {Chinburg, Ted and Guralnick, Robert and Harbater, David}, + TITLE = {Global {O}ort groups}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {473}, + YEAR = {2017}, + PAGES = {374--396}, + ISSN = {0021-8693}, + MRCLASS = {20B25 (12F10 14H30 14H37 20E34)}, + MRNUMBER = {3591155}, +MRREVIEWER = {Cheryl E. Praeger}, + DOI = {10.1016/j.jalgebra.2016.10.034}, + URL = {https://doi.org/10.1016/j.jalgebra.2016.10.034}, +} + +@article {MR2441248, + AUTHOR = {Chinburg, T. and Guralnick, R. and Harbater, D.}, + TITLE = {Oort groups and lifting problems}, + JOURNAL = {Compos. Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {144}, + YEAR = {2008}, + NUMBER = {4}, + PAGES = {849--866}, + ISSN = {0010-437X}, + MRCLASS = {14L30 (14H37)}, + MRNUMBER = {2441248}, +MRREVIEWER = {Vasily A. Chernecky}, + DOI = {10.1112/S0010437X08003515}, + URL = {https://doi.org/10.1112/S0010437X08003515}, +} + +@article {MR2919977, + AUTHOR = {Chinburg, Ted and Guralnick, Robert and Harbater, David}, + TITLE = {The local lifting problem for actions of finite groups on + curves}, + JOURNAL = {Ann. Sci. \'{E}c. Norm. Sup\'{e}r. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme + S\'{e}rie}, + VOLUME = {44}, + YEAR = {2011}, + NUMBER = {4}, + PAGES = {537--605}, + ISSN = {0012-9593}, + MRCLASS = {14H37 (12F10 14L30 20B25)}, + MRNUMBER = {2919977}, +MRREVIEWER = {Irene I. Bouw}, + DOI = {10.24033/asens.2150}, + URL = {https://doi.org/10.24033/asens.2150}, +} + +@article {MR3194816, + AUTHOR = {Pop, Florian}, + TITLE = {The {O}ort conjecture on lifting covers of curves}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {180}, + YEAR = {2014}, + NUMBER = {1}, + PAGES = {285--322}, + ISSN = {0003-486X}, + MRCLASS = {11G05 (11S15 14G32)}, + MRNUMBER = {3194816}, +MRREVIEWER = {Konstantinos Draziotis}, + DOI = {10.4007/annals.2014.180.1.6}, + URL = {https://doi.org/10.4007/annals.2014.180.1.6}, +} + +@article {MR0314846, + AUTHOR = {Manin, Ju. I.}, + TITLE = {Parabolic points and zeta functions of modular curves}, + JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.}, + FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, + VOLUME = {36}, + YEAR = {1972}, + PAGES = {19--66}, + ISSN = {0373-2436}, + MRCLASS = {14G10 (10D15 14H25)}, + MRNUMBER = {0314846}, +MRREVIEWER = {K.-B. Gundlach}, +} + +@article {MR1898372, + AUTHOR = {Manin, Yuri I. and Marcolli, Matilde}, + TITLE = {Holography principle and arithmetic of algebraic curves}, + JOURNAL = {Adv. Theor. Math. Phys.}, + FJOURNAL = {Advances in Theoretical and Mathematical Physics}, + VOLUME = {5}, + YEAR = {2001}, + NUMBER = {3}, + PAGES = {617--650}, + ISSN = {1095-0761}, + MRCLASS = {14G40 (11G35 83C47)}, + MRNUMBER = {1898372}, +MRREVIEWER = {Carlo Gasbarri}, + DOI = {10.4310/ATMP.2001.v5.n3.a6}, + URL = {https://doi.org/10.4310/ATMP.2001.v5.n3.a6}, +} + + +@book {Korchm, + AUTHOR = {Hirschfeld, J. W. P. and Korchm\'{a}ros, G. and Torres, F.}, + TITLE = {Algebraic curves over a finite field}, + SERIES = {Princeton Series in Applied Mathematics}, + PUBLISHER = {Princeton University Press, Princeton, NJ}, + YEAR = {2008}, + PAGES = {xx+696}, + ISBN = {978-0-691-09679-7}, + MRCLASS = {14G15 (11G20 11T71 14-01 14C20 14Hxx)}, + MRNUMBER = {2386879}, +MRREVIEWER = {C\'{i}cero Carvalho}, +} + +@article {maxGarciaTorres, + AUTHOR = {Fuhrmann, Rainer and Garcia, Arnaldo and Torres, Fernando}, + TITLE = {On maximal curves}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {67}, + YEAR = {1997}, + NUMBER = {1}, + PAGES = {29--51}, + ISSN = {0022-314X}, + MRCLASS = {11G20 (11R58 14G15)}, + MRNUMBER = {1485426}, +MRREVIEWER = {Gabriel D. Villa-Salvador}, + DOI = {10.1006/jnth.1997.2148}, + URL = {https://doi.org/10.1006/jnth.1997.2148}, +} + +@article {GSXcomp, + AUTHOR = {Garcia, Arnaldo and Stichtenoth, Henning and Xing, Chao-Ping}, + TITLE = {On subfields of the {H}ermitian function field}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {120}, + YEAR = {2000}, + NUMBER = {2}, + PAGES = {137--170}, + ISSN = {0010-437X}, + MRCLASS = {11R58 (11G20 14G15)}, + MRNUMBER = {1739176}, +MRREVIEWER = {Gabriel D. Villa-Salvador}, + DOI = {10.1023/A:1001736016924}, + URL = {https://doi.org/10.1023/A:1001736016924}, +} + +@incollection {MR1667946, + AUTHOR = {H\o holdt, Tom and van Lint, Jacobus H. and Pellikaan, Ruud}, + TITLE = {Algebraic geometry codes}, + BOOKTITLE = {Handbook of coding theory, {V}ol. {I}, {II}}, + PAGES = {871--961}, + PUBLISHER = {North-Holland, Amsterdam}, + YEAR = {1998}, + MRCLASS = {94-02 (94B27)}, + MRNUMBER = {1667946}, +} + +@book {MR1029027, + AUTHOR = {Goppa, V. D.}, + TITLE = {Geometry and codes}, + SERIES = {Mathematics and its Applications (Soviet Series)}, + VOLUME = {24}, + NOTE = {Translated from the Russian by N. G. Shartse}, + PUBLISHER = {Kluwer Academic Publishers Group, Dordrecht}, + YEAR = {1988}, + PAGES = {x+157}, + ISBN = {90-277-2776-7}, + MRCLASS = {14G15 (11T71 94-02 94Bxx)}, + MRNUMBER = {1029027}, +MRREVIEWER = {H. Mizuno}, + DOI = {10.1007/978-94-015-6870-8}, + URL = {https://doi.org/10.1007/978-94-015-6870-8}, +} + +@article {MR1325513, + AUTHOR = {Hansen, Johan P. and Stichtenoth, Henning}, + TITLE = {Group codes on certain algebraic curves with many rational + points}, + JOURNAL = {Appl. Algebra Engrg. Comm. Comput.}, + FJOURNAL = {Applicable Algebra in Engineering, Communication and + Computing}, + VOLUME = {1}, + YEAR = {1990}, + NUMBER = {1}, + PAGES = {67--77}, + ISSN = {0938-1279}, + MRCLASS = {94B27 (14G15 14H99)}, + MRNUMBER = {1325513}, +MRREVIEWER = {J. W. P. Hirschfeld}, + DOI = {10.1007/BF01810849}, + URL = {https://doi.org/10.1007/BF01810849}, +} + +@incollection {MR2775619, + AUTHOR = {Fanali, Stefania}, + TITLE = {On linear codes from maximal curves}, + BOOKTITLE = {Cryptography and coding}, + SERIES = {Lecture Notes in Comput. Sci.}, + VOLUME = {5921}, + PAGES = {91--111}, + PUBLISHER = {Springer, Berlin}, + YEAR = {2009}, + MRCLASS = {94B05 (14G50 94B27)}, + MRNUMBER = {2775619}, +MRREVIEWER = {Victor. A. Zinoviev}, + DOI = {10.1007/978-3-642-10868-6_7}, + URL = {https://doi.org/10.1007/978-3-642-10868-6_7}, +} + +@article {MR2002939, + AUTHOR = {Carvalho, C\'{i}cero and Torres, Fernando}, + TITLE = {On numerical semigroups related to covering of curves}, + JOURNAL = {Semigroup Forum}, + FJOURNAL = {Semigroup Forum}, + VOLUME = {67}, + YEAR = {2003}, + NUMBER = {3}, + PAGES = {344--354}, + ISSN = {0037-1912}, + MRCLASS = {14H55 (14N30 20M14)}, + MRNUMBER = {2002939}, +MRREVIEWER = {Daniele Struppa}, + DOI = {10.1007/s00233-002-0026-0}, + URL = {https://doi.org/10.1007/s00233-002-0026-0}, +} + +@article {MR1265917, + AUTHOR = {Torres, Fernando}, + TITLE = {Weierstrass points and double coverings of curves. {W}ith + application: symmetric numerical semigroups which cannot be + realized as {W}eierstrass semigroups}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {83}, + YEAR = {1994}, + NUMBER = {1}, + PAGES = {39--58}, + ISSN = {0025-2611}, + MRCLASS = {14H55 (30F20)}, + MRNUMBER = {1265917}, +MRREVIEWER = {R. F. Lax}, + DOI = {10.1007/BF02567599}, + URL = {https://doi.org/10.1007/BF02567599}, +} + +@article {MR1351128, + AUTHOR = {Torres, Fernando}, + TITLE = {On certain {$N$}-sheeted coverings of curves and numerical + semigroups which cannot be realized as {W}eierstrass + semigroups}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {23}, + YEAR = {1995}, + NUMBER = {11}, + PAGES = {4211--4228}, + ISSN = {0092-7872}, + MRCLASS = {14H55}, + MRNUMBER = {1351128}, +MRREVIEWER = {Letterio Gatto}, + DOI = {10.1080/00927879508825458}, + URL = {https://doi.org/10.1080/00927879508825458}, +} + + +@artcile{BumpNotes, +AUTHOR = {Bump, Daniel }, + TITLE = {Hecke Algebras}, + JOURNAL = {online notes, \url{http://sporadic.stanford.edu/bump/math263/hecke.pdf}} +} + +@article {MR0059914, + AUTHOR = {Shephard, G. C. and Todd, J. A.}, + TITLE = {Finite unitary reflection groups}, + JOURNAL = {Canadian J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {6}, + YEAR = {1954}, + PAGES = {274--304}, + ISSN = {0008-414X}, + MRCLASS = {20.0X}, + MRNUMBER = {0059914}, +MRREVIEWER = {H. S. M. Coxeter}, + DOI = {10.4153/cjm-1954-028-3}, + URL = {https://doi.org/10.4153/cjm-1954-028-3}, +} + + +@article {MR1637497, + AUTHOR = {Brou\'{e}, Michel and Malle, Gunter and Rouquier, Rapha\"{e}l}, + TITLE = {Complex reflection groups, braid groups, {H}ecke algebras}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {500}, + YEAR = {1998}, + PAGES = {127--190}, + ISSN = {0075-4102}, + MRCLASS = {20F55 (20C05 20F36)}, + MRNUMBER = {1637497}, +MRREVIEWER = {Arjeh M. Cohen}, +} + +@book {MR2548205, + AUTHOR = {Szamuely, Tam\'{a}s}, + TITLE = {Galois groups and fundamental groups}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {117}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2009}, + PAGES = {x+270}, + ISBN = {978-0-521-88850-9}, + MRCLASS = {14H30 (11-02 12F10 14G32)}, + MRNUMBER = {2548205}, +MRREVIEWER = {Swaminathan Subramanian}, + DOI = {10.1017/CBO9780511627064}, + URL = {https://doi.org/10.1017/CBO9780511627064}, +} + + + + + + +@article {MR1581526, + AUTHOR = {Witt, Ernst}, + TITLE = {Zyklische {K}\"{o}rper und {A}lgebren der {C}harakteristik {$p$} + vom {G}rad {$p^n$}. {S}truktur diskret bewerteter perfekter + {K}\"{o}rper mit vollkommenem {R}estklassenk\"{o}rper der + {C}harakteristik {$p$}}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {176}, + YEAR = {1937}, + PAGES = {126--140}, + ISSN = {0075-4102}, + MRCLASS = {DML}, + MRNUMBER = {1581526}, + DOI = {10.1515/crll.1937.176.126}, + URL = {https://doi.org/10.1515/crll.1937.176.126}, +} + + + +@ARTICLE{Rabinoff2014-dy, + title = "The Theory of Witt Vectors", + author = "Rabinoff, Joseph", + abstract = "This is an introduction to the theory of Witt vectors. It + includes a construction of the Witt rings, the Frobenius and + Verschiebung endomorphisms, the canonical map from W to W^2 + (its lambda-algebra structure), the relation to strict + p-rings, and an account of the Artin-Hasse exponential.", + month = sep, + year = 2014, + url = "http://arxiv.org/abs/1409.7445", + archivePrefix = "arXiv", + eprint = "1409.7445", + primaryClass = "math.NT", + arxivid = "1409.7445" +} + + +@article {MR0132067, + AUTHOR = {Serre, Jean-Pierre}, + TITLE = {Exemples de vari\'{e}t\'{e}s projectives en caract\'{e}ristique {$p$} non + relevables en caract\'{e}ristique z\'{e}ro}, + JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.}, + FJOURNAL = {Proceedings of the National Academy of Sciences of the United + States of America}, + VOLUME = {47}, + YEAR = {1961}, + PAGES = {108--109}, + ISSN = {0027-8424}, + MRCLASS = {14.08}, + MRNUMBER = {0132067}, +MRREVIEWER = {I. Barsotti}, + DOI = {10.1073/pnas.47.1.108}, + URL = {https://doi.org/10.1073/pnas.47.1.108}, +} + +@book {MR2247603, + AUTHOR = {Sernesi, Edoardo}, + TITLE = {Deformations of algebraic schemes}, + SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {334}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2006}, + PAGES = {xii+339}, + ISBN = {978-3-540-30608-5; 3-540-30608-0}, + MRCLASS = {14D15 (14B05 14B10 14B12 14B20 14B25 14D20)}, + MRNUMBER = {2247603}, +MRREVIEWER = {Marko Roczen}, +} + +@book {MR2583634, + AUTHOR = {Hartshorne, Robin}, + TITLE = {Deformation theory}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {257}, + PUBLISHER = {Springer, New York}, + YEAR = {2010}, + PAGES = {viii+234}, + ISBN = {978-1-4419-1595-5}, + MRCLASS = {14D15 (13D10 14B07 14B12)}, + MRNUMBER = {2583634}, +MRREVIEWER = {Arvid Siqveland}, + DOI = {10.1007/978-1-4419-1596-2}, + URL = {https://doi.org/10.1007/978-1-4419-1596-2}, +} + +@incollection {MR927980, + AUTHOR = {Oort, Frans}, + TITLE = {Lifting algebraic curves, abelian varieties, and their + endomorphisms to characteristic zero}, + BOOKTITLE = {Algebraic geometry, {B}owdoin, 1985 ({B}runswick, {M}aine, + 1985)}, + SERIES = {Proc. Sympos. Pure Math.}, + VOLUME = {46}, + PAGES = {165--195}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {1987}, + MRCLASS = {14K10 (11G10 14H10)}, + MRNUMBER = {927980}, +MRREVIEWER = {Tsutomu Sekiguchi}, + DOI = {10.1090/pspum/046.2/927980}, + URL = {https://doi.org/10.1090/pspum/046.2/927980}, +} + +@article {MR1011987, + AUTHOR = {Sekiguchi, T. and Oort, F. and Suwa, N.}, + TITLE = {On the deformation of {A}rtin-{S}chreier to {K}ummer}, + JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme + S\'{e}rie}, + VOLUME = {22}, + YEAR = {1989}, + NUMBER = {3}, + PAGES = {345--375}, + ISSN = {0012-9593}, + MRCLASS = {14L15 (11G20)}, + MRNUMBER = {1011987}, + URL = {http://www.numdam.org/item?id=ASENS_1989_4_22_3_345_0}, +} + +@article {MR1084537, + AUTHOR = {Shafarevich, I. R.}, + TITLE = {Abelian and nonabelian mathematics}, + NOTE = {Translated from the Russian by Smilka Zdravkovska}, + JOURNAL = {Math. Intelligencer}, + FJOURNAL = {The Mathematical Intelligencer}, + VOLUME = {13}, + YEAR = {1991}, + NUMBER = {1}, + PAGES = {67--75}, + ISSN = {0343-6993}, + MRCLASS = {01A60 (11-01)}, + MRNUMBER = {1084537}, +MRREVIEWER = {G. Eisenreich}, + DOI = {10.1007/BF03024075}, + URL = {https://doi.org/10.1007/BF03024075}, +} + +@book {MR2435235, + AUTHOR = {Kassel, Christian and Turaev, Vladimir}, + TITLE = {Braid groups}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {247}, + NOTE = {With the graphical assistance of Olivier Dodane}, + PUBLISHER = {Springer, New York}, + YEAR = {2008}, + PAGES = {xii+340}, + ISBN = {978-0-387-33841-5}, + MRCLASS = {20F36 (20C08 20F10 20F60 20M05 55R80 57M25 57M50)}, + MRNUMBER = {2435235}, +MRREVIEWER = {Stephen P. Humphries}, + DOI = {10.1007/978-0-387-68548-9}, + URL = {https://doi.org/10.1007/978-0-387-68548-9}, +} + +@article {MR1643304, + AUTHOR = {Kontogeorgis, Aristides}, + TITLE = {The group of automorphisms of the function fields of the curve + {$x^n+y^m+1=0$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {72}, + YEAR = {1998}, + NUMBER = {1}, + PAGES = {110--136}, + ISSN = {0022-314X}, + MRCLASS = {11G20 (14E09 14H05)}, + MRNUMBER = {1643304}, +MRREVIEWER = {Pavlos Tzermias}, + DOI = {10.1006/jnth.1998.2251}, + URL = {https://doi.org/10.1006/jnth.1998.2251}, +} + +@book {MR2690176, + AUTHOR = {Towse, Christopher Wayne}, + TITLE = {Weierstrass points on cyclic covers of the projective line}, + NOTE = {Thesis (Ph.D.)--Brown University}, + PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, + YEAR = {1993}, + PAGES = {85}, + MRCLASS = {Thesis}, + MRNUMBER = {2690176}, + URL = + {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:9407053}, +} + + +@book {MR1727844, + AUTHOR = {Bourbaki, Nicolas}, + TITLE = {Algebra {I}. {C}hapters 1--3}, + SERIES = {Elements of Mathematics (Berlin)}, + NOTE = {Translated from the French, + Reprint of the 1989 English translation [ MR0979982 + (90d:00002)]}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1998}, + PAGES = {xxiv+709}, + ISBN = {3-540-64243-9}, + MRCLASS = {00A05}, + MRNUMBER = {1727844}, +} + +@incollection {MR1851201, + AUTHOR = {Komatsu, Hiroaki}, + TITLE = {The module of differentials of a noncommutative ring + extension}, + BOOKTITLE = {International {S}ymposium on {R}ing {T}heory ({K}yongju, + 1999)}, + SERIES = {Trends Math.}, + PAGES = {171--177}, + PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, + YEAR = {2001}, + MRCLASS = {16W25 (16H05)}, + MRNUMBER = {1851201}, +} + +@article {MR2512636, + AUTHOR = {Tabuada, Gon\c{c}alo}, + TITLE = {Non-commutative {A}ndr\'{e}-{Q}uillen cohomology for differential + graded categories}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {321}, + YEAR = {2009}, + NUMBER = {10}, + PAGES = {2926--2942}, + ISSN = {0021-8693}, + MRCLASS = {18G60 (13D02 13D03)}, + MRNUMBER = {2512636}, +MRREVIEWER = {Andrea Solotar}, + DOI = {10.1016/j.jalgebra.2008.12.027}, + URL = {https://doi.org/10.1016/j.jalgebra.2008.12.027}, +} + +@MISC {MathOver53249, + TITLE = {snake lemma in category of groups}, + AUTHOR = {Auguste Hoang Duc (https://mathoverflow.net/users/10427/auguste-hoang-duc)}, + HOWPUBLISHED = {MathOverflow}, + NOTE = {URL:https://mathoverflow.net/q/53249 (version: 2011-01-25)}, + EPRINT = {https://mathoverflow.net/q/53249}, + URL = {https://mathoverflow.net/q/53249} +} + +@incollection {MR0257068, + AUTHOR = {Quillen, Daniel}, + TITLE = {On the (co-) homology of commutative rings}, + BOOKTITLE = {Applications of {C}ategorical {A}lgebra ({P}roc. {S}ympos. + {P}ure {M}ath., {V}ol. {XVII}, {N}ew {Y}ork, 1968)}, + PAGES = {65--87}, + PUBLISHER = {Amer. Math. Soc., Providence, R.I.}, + YEAR = {1970}, + MRCLASS = {13.90 (18.00)}, + MRNUMBER = {0257068}, +MRREVIEWER = {S. Yuan}, +} + +@book {MR0352220, + AUTHOR = {Andr\'{e}, Michel}, + TITLE = {Homologie des alg\`ebres commutatives}, + NOTE = {Die Grundlehren der mathematischen Wissenschaften, Band 206}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1974}, + PAGES = {xv+341}, + MRCLASS = {18H20 (14D15 13DXX 12GXX)}, + MRNUMBER = {0352220}, +MRREVIEWER = {R. M. Fossum}, +} + +@incollection {MR2355775, + AUTHOR = {Iyengar, Srikanth}, + TITLE = {Andr\'{e}-{Q}uillen homology of commutative algebras}, + BOOKTITLE = {Interactions between homotopy theory and algebra}, + SERIES = {Contemp. Math.}, + VOLUME = {436}, + PAGES = {203--234}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {2007}, + MRCLASS = {13D03}, + MRNUMBER = {2355775}, +MRREVIEWER = {Atabey Kaygun}, + DOI = {10.1090/conm/436/08410}, + URL = {https://doi.org/10.1090/conm/436/08410}, +} + + + + +@artcile{ParamPartA19, +AUTHOR = {Kontogeorgis, Aristides and Panagiotis Paramatzoglou }, + TITLE = {Group actions on cyclic covers of the projective line}, + Year = {2018}, + url = {arXiv:1804.07021}, +} + +@artcile{ParamPartC19, +AUTHOR = {Kontogeorgis, Aristides and Panagiotis Paramatzoglou }, + TITLE = {A non-commutative differential module approach to {A}lexander modules}, + Year = {2019}, + url = {arXiv:1904.06665} +} + +@misc{1905.04298, +Author = {Aristides Kontogeorgis and Panagiotis Paramantzoglou}, +Title = {Galois action on homology of generalized Fermat Curves}, +Year = {2019}, +url = {arXiv:1905.04298}, +} + + + + +@book {MR2103875, + AUTHOR = {Eisenbud, David}, + TITLE = {The geometry of syzygies}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {229}, + NOTE = {A second course in commutative algebra and algebraic geometry}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2005}, + PAGES = {xvi+243}, + ISBN = {0-387-22215-4}, + MRCLASS = {13D02 (13-02 13D40 14H45 14H51)}, + MRNUMBER = {2103875}, +MRREVIEWER = {Juan C. Migliore}, +} + + +@misc{milneAV, +author={Milne, James S.}, +title={Abelian Varieties (v2.00)}, +year={2008}, +note={Available at www.jmilne.org/math/}, +pages={166+vi} +} + +@incollection {MR861974, + AUTHOR = {Milne, J. S.}, + TITLE = {Abelian varieties}, + BOOKTITLE = {Arithmetic geometry ({S}torrs, {C}onn., 1984)}, + PAGES = {103--150}, + PUBLISHER = {Springer, New York}, + YEAR = {1986}, + MRCLASS = {14K05 (11G10)}, + MRNUMBER = {861974}, +} + +@article {MR3549183, + AUTHOR = {Arias-de-Reyna, Sara and Armana, C\'{e}cile and Karemaker, + Valentijn and Rebolledo, Marusia and Thomas, Lara and Vila, + N\'{u}ria}, + TITLE = {Large {G}alois images for {J}acobian varieties of genus 3 + curves}, + JOURNAL = {Acta Arith.}, + FJOURNAL = {Acta Arithmetica}, + VOLUME = {174}, + YEAR = {2016}, + NUMBER = {4}, + PAGES = {339--366}, + ISSN = {0065-1036}, + MRCLASS = {11F80 (11G10 11G30 12F12)}, + MRNUMBER = {3549183}, +MRREVIEWER = {Chun Yin Hui}, +} + +@phdthesis{Duarte, + author = {Lemos, Pedro}, + title = {Residual Representations of Abelian Varieties}, + school = {University of Warwick}, + year = {2017}, + note = {Available at http://wrap.warwick.ac.uk/94788/} +} + +@misc{nlab:five_lemma, + author = {{nLab authors}}, + title = {five lemma}, + url = {http://ncatlab.org/nlab/revision/five%20lemma/21}, + month = mar, + year = 2019 +} + +@incollection {MR3525467, + AUTHOR = {Berkesch, Christine and Schreyer, Frank-Olaf}, + TITLE = {Syzygies, finite length modules, and random curves}, + BOOKTITLE = {Commutative algebra and noncommutative algebraic geometry. + {V}ol. {I}}, + SERIES = {Math. Sci. Res. Inst. Publ.}, + VOLUME = {67}, + PAGES = {25--52}, + PUBLISHER = {Cambridge Univ. Press, New York}, + YEAR = {2015}, + MRCLASS = {13P10 (13C40 13D05 14E08 14H10 14Q05)}, + MRNUMBER = {3525467}, +MRREVIEWER = {Haohao Wang}, +} + +@article {MR1273472, + AUTHOR = {Bayer, Dave and Eisenbud, David}, + TITLE = {Ribbons and their canonical embeddings}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {347}, + YEAR = {1995}, + NUMBER = {3}, + PAGES = {719--756}, + ISSN = {0002-9947}, + MRCLASS = {14H45 (13D02 14C20)}, + MRNUMBER = {1273472}, +MRREVIEWER = {Gunnar Fl\o ystad}, + DOI = {10.2307/2154871}, + URL = {https://doi.org/10.2307/2154871}, +} + + +@incollection {MR524365, + AUTHOR = {Reiner, Irving}, + TITLE = {Integral representations of cyclic {$p$}-groups}, + BOOKTITLE = {Topics in algebra ({P}roc. 18th {S}ummer {R}es. {I}nst., + {A}ustral. {M}ath. {S}oc., {A}ustral. {N}at. {U}niv., + {C}anberra, 1978)}, + SERIES = {Lecture Notes in Math.}, + VOLUME = {697}, + PAGES = {70--87}, + PUBLISHER = {Springer, Berlin}, + YEAR = {1978}, + MRCLASS = {20C10}, + MRNUMBER = {524365}, +MRREVIEWER = {Ken-Ichi Tahara}, +} + +@misc {knotatlas, +Author = {Bar-Natan, Dror and Morrison, Scott and et al.}, +title = {The {K}not {A}tlas}, +url = {http://katlas.org}, +} + +@book {MR2768284, + AUTHOR = {Terras, Audrey}, + TITLE = {Zeta functions of graphs}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {128}, + NOTE = {A stroll through the garden}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2011}, + PAGES = {xii+239}, + ISBN = {978-0-521-11367-0}, + MRCLASS = {05-02 (05C25 11M41)}, + MRNUMBER = {2768284}, +MRREVIEWER = {Christopher Knox Storm}, +} + +@book {VakilSea, + AUTHOR = {Ravi Vakil}, + TITLE = {The rising sea}, + YEAR = {2017}, + PAGES = {775}, +} + +@book {MR1311028, + AUTHOR = {Ziegler, G\"{u}nter M.}, + TITLE = {Lectures on polytopes}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {152}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1995}, + PAGES = {x+370}, + ISBN = {0-387-94365-X}, + MRCLASS = {52Bxx}, + MRNUMBER = {1311028}, +MRREVIEWER = {Margaret M. Bayer}, + DOI = {10.1007/978-1-4613-8431-1}, + URL = {https://doi.org/10.1007/978-1-4613-8431-1}, +} + +@book {MR2014407, + AUTHOR = {Akivis, Maks A. and Goldberg, Vladislav V.}, + TITLE = {Differential geometry of varieties with degenerate {G}auss + maps}, + SERIES = {CMS Books in Mathematics/Ouvrages de Math\'{e}matiques de la SMC}, + VOLUME = {18}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2004}, + PAGES = {xxii+255}, + ISBN = {0-387-40463-5}, + MRCLASS = {53A20 (53B25)}, + MRNUMBER = {2014407}, +MRREVIEWER = {Jean-Marc Schlenker}, + DOI = {10.1007/b97221}, + URL = {https://doi.org/10.1007/b97221}, +} + +@incollection {MR1247282, + AUTHOR = {Gel\cprime fand, I. M. and Kapranov, M. M.}, + TITLE = {On the dimension and degree of the projective dual variety: a + {$q$}-analog of the {K}atz-{K}leiman formula}, + BOOKTITLE = {The {G}el\cprime fand {M}athematical {S}eminars, 1990--1992}, + PAGES = {27--33}, + PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, + YEAR = {1993}, + MRCLASS = {14N10 (14N05)}, + MRNUMBER = {1247282}, +MRREVIEWER = {Ciro Ciliberto}, +} + +@incollection {MR555696, + AUTHOR = {Holme, Audun}, + TITLE = {On the dual of a smooth variety}, + BOOKTITLE = {Algebraic geometry ({P}roc. {S}ummer {M}eeting, {U}niv. + {C}openhagen, {C}openhagen, 1978)}, + SERIES = {Lecture Notes in Math.}, + VOLUME = {732}, + PAGES = {144--156}, + PUBLISHER = {Springer, Berlin}, + YEAR = {1979}, + MRCLASS = {14N10 (14C17)}, + MRNUMBER = {555696}, +MRREVIEWER = {I. Dolgachev}, +} + +@book {MR0354657, + TITLE = {Groupes de monodromie en g\'{e}om\'{e}trie alg\'{e}brique. {II}}, + SERIES = {Lecture Notes in Mathematics, Vol. 340}, + NOTE = {S\'{e}minaire de G\'{e}om\'{e}trie Alg\'{e}brique du Bois-Marie 1967--1969 + (SGA 7 II), + Dirig\'{e} par P. Deligne et N. Katz}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1973}, + PAGES = {x+438}, + MRCLASS = {14-06}, + MRNUMBER = {0354657}, +} + +@article {MR0568897, + AUTHOR = {Kleiman, Steven L.}, + TITLE = {The enumerative theory of singularities}, + BOOKTITLE = {Real and complex singularities ({P}roc. {N}inth {N}ordic + {S}ummer {S}chool/{NAVF} {S}ympos. {M}ath., {O}slo, 1976)}, + PAGES = {297--396}, + PUBLISHER = {Sijthoff and Noordhoff, Alphen aan den Rijn}, + YEAR = {1977}, + MRCLASS = {14B05 (14C10 14E15 14N10)}, + MRNUMBER = {0568897}, +MRREVIEWER = {A. A. Iarrobino, Jr.}, +} + +@book {MR1363949, + AUTHOR = {Sturmfels, Bernd}, + TITLE = {Gr\"{o}bner bases and convex polytopes}, + SERIES = {University Lecture Series}, + VOLUME = {8}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1996}, + PAGES = {xii+162}, + ISBN = {0-8218-0487-1}, + MRCLASS = {13P10 (14M25 52B20)}, + MRNUMBER = {1363949}, +MRREVIEWER = {P. Schenzel}, +} + +@book {MR2894984, + AUTHOR = {Hida, Haruzo}, + TITLE = {Geometric modular forms and elliptic curves}, + EDITION = {Second}, + PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, + YEAR = {2012}, + PAGES = {xiv+454}, + ISBN = {978-981-4368-64-3; 981-4368-64-4}, + MRCLASS = {11F33 (11F80 11G05)}, + MRNUMBER = {2894984}, +} + +@article {MR3361016, + AUTHOR = {K\"{o}ck, Bernhard and Tait, Joseph}, + TITLE = {Faithfulness of actions on {R}iemann-{R}och spaces}, + JOURNAL = {Canad. J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {67}, + YEAR = {2015}, + NUMBER = {4}, + PAGES = {848--869}, + ISSN = {0008-414X}, + MRCLASS = {14L30 (11R32 14H30 30F30)}, + MRNUMBER = {3361016}, +MRREVIEWER = {Scott R. Nollet}, + DOI = {10.4153/CJM-2014-015-2}, + URL = {https://doi.org/10.4153/CJM-2014-015-2}, +} + + + +@article {MR494707, + AUTHOR = {Goto, Shiro and Watanabe, Keiichi}, + TITLE = {On graded rings. {I}}, + JOURNAL = {J. Math. Soc. Japan}, + FJOURNAL = {Journal of the Mathematical Society of Japan}, + VOLUME = {30}, + YEAR = {1978}, + NUMBER = {2}, + PAGES = {179--213}, + ISSN = {0025-5645}, + MRCLASS = {13H10 (13D03 14B15)}, + MRNUMBER = {494707}, +MRREVIEWER = {Gerald S. Garfinkel}, + DOI = {10.2969/jmsj/03020179}, + URL = {https://doi.org/10.2969/jmsj/03020179}, +} + +@book {MR0274461, + AUTHOR = {Altman, Allen and Kleiman, Steven}, + TITLE = {Introduction to {G}rothendieck duality theory}, + SERIES = {Lecture Notes in Mathematics, Vol. 146}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1970}, + PAGES = {ii+185}, + MRCLASS = {14.55}, + MRNUMBER = {0274461}, +MRREVIEWER = {Y. Nakai}, +} + +@book {MR2560561, + AUTHOR = {Peeva, Irena}, + TITLE = {Graded syzygies}, + SERIES = {Algebra and Applications}, + VOLUME = {14}, + PUBLISHER = {Springer-Verlag London, Ltd., London}, + YEAR = {2011}, + PAGES = {xii+302}, + ISBN = {978-0-85729-176-9}, + MRCLASS = {13D02 (05E40 13D40 13F55 14M25)}, + MRNUMBER = {2560561}, +MRREVIEWER = {Christopher A. Francisco}, + DOI = {10.1007/978-0-85729-177-6}, + URL = {https://doi.org/10.1007/978-0-85729-177-6}, +} + +@incollection {MR3729076, + AUTHOR = {Farkas, Gavril}, + TITLE = {Progress on syzygies of algebraic curves}, + BOOKTITLE = {Moduli of curves}, + SERIES = {Lect. Notes Unione Mat. Ital.}, + VOLUME = {21}, + PAGES = {107--138}, + PUBLISHER = {Springer, Cham}, + YEAR = {2017}, + MRCLASS = {14H10 (13D02)}, + MRNUMBER = {3729076}, +MRREVIEWER = {Haohao Wang}, +} + + + +@article{1803.10481, +author = {Christian Bopp and Frank-Olaf Schreyer}, +title = {A Version of Green's Conjecture in Positive Characteristic}, +journal = {Experimental Mathematics}, +volume = {0}, +number = {0}, +pages = {1-6}, +year = {2019}, +publisher = {Taylor & Francis}, +doi = {10.1080/10586458.2019.1576082}, +URL = { + https://doi.org/10.1080/10586458.2019.1576082 + +}, +eprint = { + https://doi.org/10.1080/10586458.2019.1576082 +} +} + + + +@incollection {MR3916740, + AUTHOR = {Broughton, A. and Shaska, T. and Wootton, A.}, + TITLE = {On automorphisms of algebraic curves}, + BOOKTITLE = {Algebraic curves and their applications}, + SERIES = {Contemp. Math.}, + VOLUME = {724}, + PAGES = {175--212}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {2019}, + MRCLASS = {14H37 (14H45)}, + MRNUMBER = {3916740}, + DOI = {10.1090/conm/724/14590}, + URL = {https://doi.org/10.1090/conm/724/14590}, +} + +@incollection {MR895152, + AUTHOR = {Green, Mark and Lazarsfeld, Robert}, + TITLE = {A simple proof of {P}etri's theorem on canonical curves}, + BOOKTITLE = {Geometry today ({R}ome, 1984)}, + SERIES = {Progr. Math.}, + VOLUME = {60}, + PAGES = {129--142}, + PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, + YEAR = {1985}, + MRCLASS = {14H45 (14C20)}, + MRNUMBER = {895152}, +MRREVIEWER = {Ciro Ciliberto}, +} + +@book {MR2267317, + AUTHOR = {Benson, David J.}, + TITLE = {Modular representation theory}, + SERIES = {Lecture Notes in Mathematics}, + VOLUME = {1081}, + NOTE = {New trends and methods, + Second printing of the 1984 original}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2006}, + PAGES = {xii+231}, + ISBN = {978-3-540-13389-6; 3-540-13389-5}, + MRCLASS = {20C20 (20-01)}, + MRNUMBER = {2267317}, +} + +@article {MR3069500, + AUTHOR = {Hecke, E.}, + TITLE = {\"{U}ber ein fundamentalproblem aus der theorie der elliptischen + modulfunktionen}, + JOURNAL = {Abh. Math. Sem. Univ. Hamburg}, + FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t + Hamburg}, + VOLUME = {6}, + YEAR = {1928}, + NUMBER = {1}, + PAGES = {235--257}, + ISSN = {0025-5858}, + MRCLASS = {DML}, + MRNUMBER = {3069500}, + DOI = {10.1007/BF02940613}, + URL = {https://doi.org/10.1007/BF02940613}, +} + + + + +@article {1901.08446, + AUTHOR = {Kontogeorgis, Aristides and Tsouknidas, Ioannis}, + TITLE = {A cohomological treatise of {HKG}-covers with applications to + the {N}ottingham group}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {555}, + YEAR = {2020}, + PAGES = {325--345}, + ISSN = {0021-8693}, + MRCLASS = {14H30 (20E18 20J06)}, + MRNUMBER = {4081494}, + DOI = {10.1016/j.jalgebra.2020.02.037}, + URL = {https://doi.org/10.1016/j.jalgebra.2020.02.037}, +} + + + + + +@article{MediterKTS, + AUTHOR = {Kontogeorgis, Aristides and Terezakis, Alexios and Tsouknidas, + Ioannis}, + TITLE = {Automorphisms and the {C}anonical {I}deal}, + JOURNAL = {Mediterr. J. Math.}, + FJOURNAL = {Mediterranean Journal of Mathematics}, + VOLUME = {18}, + YEAR = {2021}, + NUMBER = {6}, + PAGES = {Paper No. 261}, + ISSN = {1660-5446}, + MRCLASS = {14 (13)}, + MRNUMBER = {4333646}, + DOI = {10.1007/s00009-021-01878-3}, + URL = {https://doi.org/10.1007/s00009-021-01878-3}, +} + + +@book {MR1343250, + AUTHOR = {Fulton, William}, + TITLE = {Algebraic topology}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {153}, + NOTE = {A first course}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1995}, + PAGES = {xviii+430}, + ISBN = {0-387-94326-9; 0-387-94327-7}, + MRCLASS = {55-01 (30-01 57-01)}, + MRNUMBER = {1343250}, +MRREVIEWER = {Ross Geoghegan}, + DOI = {10.1007/978-1-4612-4180-5}, + URL = {https://doi.org/10.1007/978-1-4612-4180-5}, +} + + + +@article {Belyi2, + AUTHOR = {Bely{\u\i}, G. V.}, + TITLE = {A new proof of the three-point theorem}, + JOURNAL = {Mat. Sb.}, + FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Matematicheski\u\i\ Sbornik}, + VOLUME = {193}, + YEAR = {2002}, + NUMBER = {3}, + PAGES = {21--24}, + ISSN = {0368-8666}, + MRCLASS = {14G25 (14H30)}, + MRNUMBER = {1913596 (2003b:14030)}, + DOI = {10.1070/SM2002v193n03ABEH000633}, + URL = {http://dx.doi.org/10.1070/SM2002v193n03ABEH000633}, +} + + +@article {ManTor, + AUTHOR = {Manin, Ju. I.}, + TITLE = {Parabolic points and zeta functions of modular curves}, + JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.}, + FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, + VOLUME = {36}, + YEAR = {1972}, + PAGES = {19--66}, + ISSN = {0373-2436}, + MRCLASS = {14G10 (10D15 14H25)}, + MRNUMBER = {0314846 (47 \#3396)}, +MRREVIEWER = {K.-B. Gundlach}, +} + +@article {DrinTor, + AUTHOR = {Drinfel{\cprime}d, V. G.}, + TITLE = {Two theorems on modular curves}, + JOURNAL = {Funkcional. Anal. i Prilo\v zen.}, + FJOURNAL = {Akademija Nauk SSSR. Funkcional\cprime nyi Analiz i ego + Prilo\v zenija}, + VOLUME = {7}, + YEAR = {1973}, + NUMBER = {2}, + PAGES = {83--84}, + ISSN = {0374-1990}, + MRCLASS = {14G10 (10D15 14H25)}, + MRNUMBER = {0318157 (47 \#6705)}, +MRREVIEWER = {K.-B. Gundlach}, +} + +@article {RosenNorm, + AUTHOR = {Rosen, Michael}, + TITLE = {The norm map on {J}acobians}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {87}, + YEAR = {1983}, + NUMBER = {1}, + PAGES = {19--22}, + ISSN = {0002-9939}, + CODEN = {PAMYAR}, + MRCLASS = {14H30}, + MRNUMBER = {677222 (84b:14016)}, +MRREVIEWER = {Lee Rudolph}, + DOI = {10.2307/2044342}, + URL = {http://dx.doi.org/10.2307/2044342}, +} + +@article {yang:96, + AUTHOR = {Yang, Tonghai}, + TITLE = {Cusp forms of weight {$1$} associated to {F}ermat curves}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {83}, + YEAR = {1996}, + NUMBER = {1}, + PAGES = {141--156}, + ISSN = {0012-7094}, + CODEN = {DUMJAO}, + MRCLASS = {11F11 (11G18)}, + MRNUMBER = {1388846 (97e:11053)}, +MRREVIEWER = {Henri Darmon}, + DOI = {10.1215/S0012-7094-96-08306-4}, + URL = {http://dx.doi.org/10.1215/S0012-7094-96-08306-4}, +} + +@incollection {Se:Weight1, + AUTHOR = {Serre, J.-P.}, + TITLE = {Modular forms of weight one and {G}alois representations}, + BOOKTITLE = {Algebraic number fields: {$L$}-functions and {G}alois + properties ({P}roc. {S}ympos., {U}niv. {D}urham, {D}urham, + 1975)}, + PAGES = {193--268}, + PUBLISHER = {Academic Press}, + ADDRESS = {London}, + YEAR = {1977}, + MRCLASS = {10D15}, + MRNUMBER = {0450201 (56 \#8497)}, +MRREVIEWER = {Stephen Gelbart}, +} + +@article {DeSe, + AUTHOR = {Deligne, Pierre and Serre, Jean-Pierre}, + TITLE = {Formes modulaires de poids {$1$}}, + JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. + Quatri\`eme S\'erie}, + VOLUME = {7}, + YEAR = {1974}, + PAGES = {507--530 (1975)}, + ISSN = {0012-9593}, + MRCLASS = {10D15 (12A65)}, + MRNUMBER = {0379379 (52 \#284)}, +MRREVIEWER = {Stephen Gelbart}, +} + +@article {TzermiasTorsion98, + AUTHOR = {Tzermias, Pavlos}, + TITLE = {Torsion parts of {M}ordell-{W}eil groups of {F}ermat + {J}acobians}, + JOURNAL = {Internat. Math. Res. Notices}, + FJOURNAL = {International Mathematics Research Notices}, + YEAR = {1998}, + NUMBER = {7}, + PAGES = {359--369}, + ISSN = {1073-7928}, + MRCLASS = {11G30 (14G05)}, + MRNUMBER = {1623406 (99c:11078)}, +MRREVIEWER = {Dino J. Lorenzini}, + DOI = {10.1155/S1073792898000233}, + URL = {http://dx.doi.org/10.1155/S1073792898000233}, +} + +@article {TzermiasCuspidal, + AUTHOR = {Coleman, Robert F. and Tamagawa, Akio and Tzermias, Pavlos}, + TITLE = {The cuspidal torsion packet on the {F}ermat curve}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {496}, + YEAR = {1998}, + PAGES = {73--81}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {11G30 (11G10)}, + MRNUMBER = {1605810 (99b:11066)}, +MRREVIEWER = {Nguyen Khac-Viet}, + DOI = {10.1515/crll.1998.033}, + URL = {http://dx.doi.org/10.1515/crll.1998.033}, +} + +@article {wolfartCrelle, + AUTHOR = {Shiga, Hironori and Wolfart, J{\"u}rgen}, + TITLE = {Criteria for complex multiplication and transcendence + properties of automorphic functions}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik}, + VOLUME = {463}, + YEAR = {1995}, + PAGES = {1--25}, + ISSN = {0075-4102}, + CODEN = {JRMAA8}, + MRCLASS = {11G18 (11F46 11J86)}, + MRNUMBER = {1332905 (96g:11063)}, +MRREVIEWER = {Michel Waldschmidt}, + DOI = {10.1515/crll.1995.463.1}, + URL = {http://dx.doi.org/10.1515/crll.1995.463.1}, +} + + + @ARTICLE{WolfartTriangle, + title = "Triangle groups and Jacobians of {CM} type", + author = "Wolfart, J", + abstract = "In the last years, two new tools have been developed for an + approach to the question whether a given nonsingular projective + algebraic curve over a number field has a Jacobian of CM type . + First, such curves can be characterized by the existence of + Belyi functions or ...", + journal = "manuscript at http://www. math. uni-frankfurt. de/~", + publisher = "math.uni-frankfurt.de", + year = 2000 + } + + + + +@book {Stichtenothv2009, + AUTHOR = {Stichtenoth, Henning}, + TITLE = {Algebraic function fields and codes}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {254}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2009}, + PAGES = {xiv+355}, + ISBN = {978-3-540-76877-7}, + MRCLASS = {14H05 (11R58 11T71 14G15 14G50 94B27)}, + MRNUMBER = {2464941 (2010d:14034)}, +} + + + +@ARTICLE{Singerman1972-vp, + title = "Finitely Maximal Fuchsian Groups", + author = "Singerman, David", + journal = "J. Lond. Math. Soc.", + volume = "s2-6", + number = 1, + pages = "29--38", + month = "1~" # dec, + year = 1972, + url = "http://jlms.oxfordjournals.org/content/s2-6/1/29.short", + issn = "0024-6107", + doi = "10.1112/jlms/s2-6.1.29" +} + + + +@ARTICLE{Kallel2005-ru, + title = "On the group of automorphisms of cyclic covers of the {R}iemann + sphere", + author = "Kallel, Sadok and Sjerve, Denis", + journal = "Math. Proc. Cambridge Philos. Soc.", + volume = 138, + number = 2, + pages = "267--287", + year = 2005, + url = "http://www.mendeley.com/research/group-automorphisms-cyclic-covers-riemann-sphere-1/", + issn = "0305-0041" +} + + +@ARTICLE{Harrison2011-ke, + title = "A New Automorphism Of ${X}_0(108)$", + author = "Harrison, Michael Corin", + abstract = "Let X0(N) denote the modular curve classifying elliptic + curves with a cyclic N-isogeny, A0(N) its group of algebraic + autmorphisms and B0(N) the subgroup of automorphisms coming + from matrices acting on the upper halfplane. In a well-known + paper, Kenku and Momose showed that A0(N) and B0(N) are + equal (all automorphisms come from matrix action) when X0(N) + has genus at least 2, except for N = 37 and 63. However, + there is a mistake in their analysis of the N = 108 case. In + the style of Kenku and Momose, we show that B0(108) is of + index 2 in A0(108) and construct an explicit new + automorphism of order 2 on a canonical model of X0(108).", + month = "29~" # aug, + year = 2011, + url = "http://arxiv.org/abs/1108.5595", + archivePrefix = "arXiv", + eprint = "1108.5595", + primaryClass = "math.NT", + arxivid = "1108.5595" +} + + + +@ARTICLE{Kamienny2003-tg, + title = "On the automorphism groups of some modular curves", + author = "Kamienny, S", + abstract = "Let $N$ be a prime number, and $X$ a curve that is intermediate + to the cover $X_1(N)\textbackslash{}rightarrow X_0(N)$. We study + the automorphism group of $X$, and prove that in most cases it + is generated by the Galois group of the cover + $X\textbackslash{}rightarrow X_0(N)$, and any lift of the + Atkin--Lehner involution to $X$.", + journal = "Math. Proc. Cambridge Philos. Soc.", + publisher = "Cambridge University Press", + volume = 134, + number = 01, + pages = "61--64", + month = "10~" # mar, + year = 2003, + url = "http://journals.cambridge.org/abstract_S0305004102006023", + issn = "1469-8064, 1469-8064", + doi = "10.1017/S0305004102006023" +} + + + +@ARTICLE{Kenku1988-xb, + title = "Automorphism groups of the modular curves $ {X}_0 (N) $", + author = "Kenku, M A and Momose, Fumiyuki", + journal = "Compos. Math.", + volume = 65, + number = 1, + pages = "51--80", + year = 1988, + url = "http://archive.numdam.org/article/CM_1988__65_1_51_0.pdf", + issn = "0010-437X" +} + + + + +@ARTICLE{Baker2003-im, + title = "Automorphisms of $X_0^∗(p)$", + author = "Baker, Matthew and Hasegawa, Yuji", + journal = "J. Number Theory", + publisher = "Elsevier", + volume = 100, + number = 1, + pages = "72--87", + year = 2003, + url = "http://www.sciencedirect.com/science/article/pii/S0022314X02001208", + issn = "0022-314X" +} + + +@ARTICLE{Kontogeorgis2008-qp, + title = "On the non-existence of exceptional automorphisms on Shimura + curves", + author = "Kontogeorgis, Aristides and Rotger, Victor", + journal = "Bull. Lond. Math. Soc.", + volume = 40, + number = 3, + pages = "363--374", + year = 2008, + url = " + http://dx.doi.org/10.1112/blms/bdn012", + issn = "0024-6093", + doi = "10.1112/blms/bdn012" +} + + +@ARTICLE{Rotger2002-cn, + title = "On the group of automorphisms of Shimura curves and applications", + author = "Rotger, Victor", + journal = "Compos. Math.", + volume = 132, + number = 2, + pages = "229--241", + year = 2002, + url = "http://www.mendeley.com/research/group-automorphisms-shimura-curves-applications/", + issn = "0010-437X" +} + +@ARTICLE{Molina2013-ni, + title = "Automorphisms and reduction of Heegner points on Shimura curves at + {Cerednik-Drinfeld} primes", + author = "Molina, Santiago and Rotger, Victor", + journal = "Proc. Am. Math. Soc.", + volume = 142, + number = 2, + year = 2013, + url = "http://dx.doi.org/10.1090/s0002-9939-2013-11772-7", + issn = "0002-9939", + doi = "10.1090/s0002-9939-2013-11772-7" +} + + +@ARTICLE{Greenberg1963-tf, + title = "Maximal fuchsian groups", + author = "Greenberg, Leon", + journal = "Bull. Am. Math. Soc.", + volume = 69, + number = 4, + pages = "569--573", + year = 1963, + url = "http://www.ams.org/bull/1963-69-04/S0002-9904-1963-11001-0/", + issn = "0273-0979" +} + + +@ARTICLE{Greenberg1974-mz, + title = "Maximal groups and signatures", + author = "Greenberg, Leon", + journal = "Ann. of Math. Studies", + volume = 79, + pages = "207--226", + year = 1974, + url = "https://books.google.com/books?hl=en&lr=&id=oriXEV6VoM0C&oi=fnd&pg=PA207&dq=Greenberg%2Bmaximal&ots=JK1YjEakzV&sig=e06NEE18b450RXcGEHPULQJfOXs" +} + + + + +@book{beardon1995geometry, + title={The Geometry of Discrete Groups}, + author={Beardon, A.F.}, + isbn={9780387907888}, + lccn={lc82019268}, + series={Graduate Texts in Mathematics}, + url={https://books.google.gr/books?id=5\_48tS\_5KjgC}, + year={1995}, + publisher={Springer New York} +} + + + +@ARTICLE{Kock2014-ep, + title = "Faithfulness of actions on {Riemann-Roch} spaces", + author = "K{\"{o}}ck, Bernhard and Tait, Joseph", + abstract = "Given a faithful action of a finite group G on an algebraic + curve X of genus g\_X > 1, we give explicit criteria for the + induced action of G on the Riemann-Roch space H^0(X,O\_X(D)) + to be faithful, where D is a G-invariant divisor on X of + degree at least 2g\_X-2. This leads to a concise answer to + the question when the action of G on the space H^0(X, + \textbackslash{}Omega\_X^m) of global holomorphic + polydifferentials of order m is faithful. If X is + hyperelliptic, we furthermore provide an explicit basis of + H^0(X, \textbackslash{}Omega\_X^m). Finally, we give + applications in deformation theory and in coding theory and + we discuss the analogous problem for the action of G on the + first homology H\_1(X, Z/mZ) if X is a Riemann surface.", + month = 04, + year = 2014, + url = "http://arxiv.org/abs/1404.3135", + archivePrefix = "arXiv", + eprint = "1404.3135", + primaryClass = "math.AG", + arxivid = "1404.3135" +} + +@article{Baker2003-new, + AUTHOR = {Baker, Matthew and Hasegawa, Yuji}, + TITLE = {Automorphisms of {$X_0^\ast(p)$} }, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {100}, + YEAR = {2003}, + NUMBER = {1}, + PAGES = {72--87}, + ISSN = {0022-314X}, + MRCLASS = {11G18}, + MRNUMBER = {1971247}, +MRREVIEWER = {Conjeeveram S. Rajan}, + DOI = {10.1016/S0022-314X(02)00120-8}, + URL = {https://doi.org/10.1016/S0022-314X(02)00120-8}, +} + +@misc{milneMF, +author={Milne, James S.}, +title={Modular Functions and Modular Forms (v1.31)}, +year={2017}, +note={Available at www.jmilne.org/math/}, +pages={134} +} + +@book {MR2626317, + AUTHOR = {Rohrlich, David Ephraim}, + TITLE = {M{ODULAR} {FUNCTIONS} {AND} {THE} {FERMAT} {CURVES}}, + NOTE = {Thesis (Ph.D.)--Yale University}, + PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, + YEAR = {1976}, + PAGES = {107}, + MRCLASS = {Thesis}, + MRNUMBER = {2626317}, + URL = + {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7629184}, +} + +@incollection {MR1483112, + AUTHOR = {Wolfart, J\"{u}rgen}, + TITLE = {The ``obvious'' part of {B}elyi's theorem and {R}iemann + surfaces with many automorphisms}, + BOOKTITLE = {Geometric {G}alois actions, 1}, + SERIES = {London Math. Soc. Lecture Note Ser.}, + VOLUME = {242}, + PAGES = {97--112}, + PUBLISHER = {Cambridge Univ. Press, Cambridge}, + YEAR = {1997}, + MRCLASS = {14H30 (11G30 30F10)}, + MRNUMBER = {1483112}, +MRREVIEWER = {Gabino Gonz\'{a}lez Diez}, +} + +@book {MR1453580, + AUTHOR = {Yoshida, Masaaki}, + TITLE = {Hypergeometric functions, my love}, + SERIES = {Aspects of Mathematics, E32}, + NOTE = {Modular interpretations of configuration spaces}, + PUBLISHER = {Friedr. Vieweg \& Sohn, Braunschweig}, + YEAR = {1997}, + PAGES = {xvi+292}, + ISBN = {3-528-06925-2}, + MRCLASS = {33C70 (11F55 14J28 14K25 32G34 33-02 33C80)}, + MRNUMBER = {1453580}, +MRREVIEWER = {Georgi Hristov Georgiev}, + DOI = {10.1007/978-3-322-90166-8}, + URL = {https://doi.org/10.1007/978-3-322-90166-8}, +} + +@book {MR1193029, + AUTHOR = {Knapp, Anthony W.}, + TITLE = {Elliptic curves}, + SERIES = {Mathematical Notes}, + VOLUME = {40}, + PUBLISHER = {Princeton University Press, Princeton, NJ}, + YEAR = {1992}, + PAGES = {xvi+427}, + ISBN = {0-691-08559-5}, + MRCLASS = {11G05 (11-01 11F11 14H52)}, + MRNUMBER = {1193029}, +MRREVIEWER = {Joseph H. Silverman}, +} + +@book {MR2024529, + AUTHOR = {Husem\"{o}ller, Dale}, + TITLE = {Elliptic curves}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {111}, + EDITION = {Second}, + NOTE = {With appendices by Otto Forster, Ruth Lawrence and Stefan + Theisen}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2004}, + PAGES = {xxii+487}, + ISBN = {0-387-95490-2}, + MRCLASS = {11G05 (11-01 14G25 14H52 81T30 94A60)}, + MRNUMBER = {2024529}, +MRREVIEWER = {Joseph H. Silverman}, +} + +@article {MR294345, + AUTHOR = {V\'{e}lu, Jacques}, + TITLE = {Isog\'{e}nies entre courbes elliptiques}, + JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. A-B}, + FJOURNAL = {Comptes Rendus Hebdomadaires des S\'{e}ances de l'Acad\'{e}mie des + Sciences. S\'{e}ries A et B}, + VOLUME = {273}, + YEAR = {1971}, + PAGES = {A238--A241}, + ISSN = {0151-0509}, + MRCLASS = {14H99}, + MRNUMBER = {294345}, +MRREVIEWER = {J. C. Fogarty}, +} + +@manual{sage8.9, + Key = {Sage}, + Author = {W.\thinspace{}A. Stein and others}, + Organization = {The Sage Development Team}, + Title = {{S}age {M}athematics {S}oftware ({V}ersion 8.9)}, + note = {{\tt http://www.sagemath.org}}, + Year = {2019}, +} + +@Misc{M2, + author = {Grayson, Daniel R. and Stillman, Michael E.}, + title = {Macaulay2, a software system for research in algebraic geometry}, + howpublished = {Available at \url{http://www.math.uiuc.edu/Macaulay2/}} + } + +@misc{1710.09830, +Author = {Mahrud Sayrafi}, +Title = {Computations over Local Rings in Macaulay2}, +Year = {2017}, +url = {arXiv:1710.09830}, +} + + +@incollection {MR2011758, + AUTHOR = {Dumas, Jean-Guillaume and Heckenbach, Frank and Saunders, + David and Welker, Volkmar}, + TITLE = {Computing simplicial homology based on efficient {S}mith + normal form algorithms}, + BOOKTITLE = {Algebra, geometry, and software systems}, + PAGES = {177--206}, + PUBLISHER = {Springer, Berlin}, + YEAR = {2003}, + MRCLASS = {55N99 (15A21 65F30 68W30)}, + MRNUMBER = {2011758}, +} + +@book {MR770932, + AUTHOR = {Arbarello, E. and Cornalba, M. and Griffiths, P. A. and + Harris, J.}, + TITLE = {Geometry of algebraic curves. {V}ol. {I}}, + SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {267}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1985}, + PAGES = {xvi+386}, + ISBN = {0-387-90997-4}, + MRCLASS = {14Hxx (14-02)}, + MRNUMBER = {770932}, +MRREVIEWER = {Werner Kleinert}, + DOI = {10.1007/978-1-4757-5323-3}, + URL = {https://doi.org/10.1007/978-1-4757-5323-3}, +} + + +@article {MR943539, + AUTHOR = {St\"{o}hr, Karl-Otto and Viana, Paulo}, + TITLE = {A variant of {P}etri's analysis of the canonical ideal of an + algebraic curve}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {61}, + YEAR = {1988}, + NUMBER = {2}, + PAGES = {223--248}, + ISSN = {0025-2611}, + MRCLASS = {14H99 (14C20)}, + MRNUMBER = {943539}, +MRREVIEWER = {Joseph Harris}, + DOI = {10.1007/BF01259331}, + URL = {https://doi.org/10.1007/BF01259331}, +} + + + + + + + +@article {MR4117575, + AUTHOR = {Kontogeorgis, Aristides and Paramantzoglou, Panagiotis}, + TITLE = {Group {A}ctions on cyclic covers of the projective line}, + JOURNAL = {Geom. Dedicata}, + FJOURNAL = {Geometriae Dedicata}, + VOLUME = {207}, + YEAR = {2020}, + PAGES = {311--334}, + ISSN = {0046-5755}, + MRCLASS = {Prelim}, + MRNUMBER = {4117575}, + DOI = {10.1007/s10711-019-00501-w}, + URL = {https://doi.org/10.1007/s10711-019-00501-w}, +} + + +@article {MR739785, + AUTHOR = {Green, Mark L.}, + TITLE = {Koszul cohomology and the geometry of projective varieties}, + JOURNAL = {J. Differential Geom.}, + FJOURNAL = {Journal of Differential Geometry}, + VOLUME = {19}, + YEAR = {1984}, + NUMBER = {1}, + PAGES = {125--171}, + ISSN = {0022-040X}, + MRCLASS = {14F05 (14B12)}, + MRNUMBER = {739785}, +MRREVIEWER = {G. Horrocks}, + URL = {http://projecteuclid.org/euclid.jdg/1214438426}, +} + +@article {MR2157134, + AUTHOR = {Voisin, Claire}, + TITLE = {Green's canonical syzygy conjecture for generic curves of odd + genus}, + JOURNAL = {Compos. Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {141}, + YEAR = {2005}, + NUMBER = {5}, + PAGES = {1163--1190}, + ISSN = {0010-437X}, + MRCLASS = {14H51 (14C20 14F17 14J28)}, + MRNUMBER = {2157134}, +MRREVIEWER = {Montserrat Teixidor i Bigas}, + DOI = {10.1112/S0010437X05001387}, + URL = {https://doi.org/10.1112/S0010437X05001387}, +} + +@article {MR1941089, + AUTHOR = {Voisin, Claire}, + TITLE = {Green's generic syzygy conjecture for curves of even genus + lying on a {$K3$} surface}, + JOURNAL = {J. Eur. Math. Soc. (JEMS)}, + FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, + VOLUME = {4}, + YEAR = {2002}, + NUMBER = {4}, + PAGES = {363--404}, + ISSN = {1435-9855}, + MRCLASS = {14H51 (14J28)}, + MRNUMBER = {1941089}, +MRREVIEWER = {Jean D'Almeida}, + DOI = {10.1007/s100970200042}, + URL = {https://doi.org/10.1007/s100970200042}, +} + + +@article {MR347818, + AUTHOR = {Mumford, David}, + TITLE = {A remark on the paper of {M}. {S}chlessinger}, + JOURNAL = {Rice Univ. Stud.}, + FJOURNAL = {Rice University Studies}, + VOLUME = {59}, + YEAR = {1973}, + NUMBER = {1}, + PAGES = {113--117}, + ISSN = {0035-4996}, + MRCLASS = {14B05 (14D15 32C40)}, + MRNUMBER = {347818}, +MRREVIEWER = {Bernard Teissier}, +} + + + +@article {MR344519, + AUTHOR = {Schlessinger, Michael}, + TITLE = {On rigid singularities}, + JOURNAL = {Rice Univ. Stud.}, + FJOURNAL = {Rice University Studies}, + VOLUME = {59}, + YEAR = {1973}, + NUMBER = {1}, + PAGES = {147--162}, + ISSN = {0035-4996}, + MRCLASS = {32C40 (14B10)}, + MRNUMBER = {344519}, +MRREVIEWER = {Bernard Teissier}, +} + +@incollection {MR1603467, + AUTHOR = {Grothendieck, Alexander}, + TITLE = {G\'{e}om\'{e}trie formelle et g\'{e}om\'{e}trie alg\'{e}brique}, + BOOKTITLE = {S\'{e}minaire {B}ourbaki, {V}ol. 5}, + PAGES = {Exp. No. 182, 193--220, errata p. 390}, + PUBLISHER = {Soc. Math. France, Paris}, + YEAR = {1995}, + MRCLASS = {14A15}, + MRNUMBER = {1603467}, +} + + +@MISC {MO5211, + TITLE = {Geometric meaning of the {E}uler sequence on $\mathbb{P}^n$ (Example 8.20.1 in Ch II of {H}artshorne)}, + AUTHOR = {Enrique Acosta (https://mathoverflow.net/users/1724/enrique-acosta)}, + HOWPUBLISHED = {MathOverflow}, + NOTE = {URL:https://mathoverflow.net/q/5211 (version: 2016-12-11)}, + EPRINT = {https://mathoverflow.net/q/5211}, + URL = {https://mathoverflow.net/q/5211} +} + + +@book {MR883960, + AUTHOR = {Demazure, Michel}, + TITLE = {Lectures on {$p$}-divisible groups}, + SERIES = {Lecture Notes in Mathematics}, + VOLUME = {302}, + NOTE = {Reprint of the 1972 original}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1986}, + PAGES = {vi+98}, + ISBN = {3-540-06092-8}, + MRCLASS = {14L05 (11G10)}, + MRNUMBER = {883960}, +} + + +@book {MR1653294, + AUTHOR = {Lam, T. Y.}, + TITLE = {Lectures on modules and rings}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {189}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1999}, + PAGES = {xxiv+557}, + ISBN = {0-387-98428-3}, + MRCLASS = {16-01}, + MRNUMBER = {1653294}, +MRREVIEWER = {Jonathan Golan}, + DOI = {10.1007/978-1-4612-0525-8}, + URL = {https://doi.org/10.1007/978-1-4612-0525-8}, +} + +@article {MR818915, + AUTHOR = {Lubotzky, Alexander and Magid, Andy R.}, + TITLE = {Varieties of representations of finitely generated groups}, + JOURNAL = {Mem. Amer. Math. Soc.}, + FJOURNAL = {Memoirs of the American Mathematical Society}, + VOLUME = {58}, + YEAR = {1985}, + NUMBER = {336}, + PAGES = {xi+117}, + ISSN = {0065-9266}, + MRCLASS = {20C15 (14D20)}, + MRNUMBER = {818915}, +MRREVIEWER = {Avner Ash}, + DOI = {10.1090/memo/0336}, + URL = {https://doi.org/10.1090/memo/0336}, +} + + +@book {MR2807457, + AUTHOR = {Arbarello, Enrico and Cornalba, Maurizio and Griffiths, + Phillip A.}, + TITLE = {Geometry of algebraic curves. {V}olume {II}}, + SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {268}, + NOTE = {With a contribution by Joseph Daniel Harris}, + PUBLISHER = {Springer, Heidelberg}, + YEAR = {2011}, + PAGES = {xxx+963}, + ISBN = {978-3-540-42688-2}, + MRCLASS = {14H10 (32G15)}, + MRNUMBER = {2807457}, +MRREVIEWER = {E. Looijenga}, + DOI = {10.1007/978-3-540-69392-5}, + URL = {https://doi.org/10.1007/978-3-540-69392-5}, +} + + +@misc{stacks-projectFlatSes, + author = {The {Stacks project authors}}, + title = {The Stacks project}, + howpublished = {\url{https://stacks.math.columbia.edu}}, + year = {2020}, +} + + +@article {MR1043748, + AUTHOR = {Kim, Seon Jeong}, + TITLE = {On the existence of {W}eierstrass gap sequences on trigonal + curves}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {63}, + YEAR = {1990}, + NUMBER = {2}, + PAGES = {171--180}, + ISSN = {0022-4049}, + MRCLASS = {14H55 (14H30 14H45)}, + MRNUMBER = {1043748}, +MRREVIEWER = {R. F. Lax}, + DOI = {10.1016/0022-4049(90)90024-C}, + URL = {https://doi.org/10.1016/0022-4049(90)90024-C}, +} + +@article{harbater1980moduli, + Author = {Harbater, David}, + Date-Added = {2018-08-22 18:24:15 +0000}, + Date-Modified = {2018-08-22 18:24:15 +0000}, + Journal = {Communications in Algebra}, + Number = {12}, + Pages = {1095--1122}, + Publisher = {Taylor \& Francis}, + Title = {Moduli of p-covers of curves}, + Volume = {8}, + Year = {1980}} + + @article{katz1986local, + Author = {Katz, Nicholas M}, + Date-Added = {2018-08-22 18:24:37 +0000}, + Date-Modified = {2018-08-22 18:24:37 +0000}, + Journal = {Ann. Inst. Fourier (Grenoble)}, + Number = {4}, + Pages = {69--106}, + Title = {Local-to-global extensions of representations of fundamental groups}, + Volume = {36}, + Year = {1986} + } + +@article {MR1404926, + AUTHOR = {Kapovich, Michael and Millson, John J.}, + TITLE = {On the deformation theory of representations of fundamental + groups of compact hyperbolic {$3$}-manifolds}, + JOURNAL = {Topology}, + FJOURNAL = {Topology. An International Journal of Mathematics}, + VOLUME = {35}, + YEAR = {1996}, + NUMBER = {4}, + PAGES = {1085--1106}, + ISSN = {0040-9383}, + MRCLASS = {57M50 (32G13 57N10)}, + MRNUMBER = {1404926}, +MRREVIEWER = {Darren D. Long}, + DOI = {10.1016/0040-9383(95)00060-7}, + URL = {https://doi.org/10.1016/0040-9383(95)00060-7}, +} + + +@incollection {MR3748903, + AUTHOR = {Antoniadis, Jannis A. and Kontogeorgis, Aristides}, + TITLE = {Automorphisms of curves}, + BOOKTITLE = {Algebraic modeling of topological and computational structures + and applications}, + SERIES = {Springer Proc. Math. Stat.}, + VOLUME = {219}, + PAGES = {339--361}, + PUBLISHER = {Springer, Cham}, + YEAR = {2017}, + MRCLASS = {14H37 (14G17)}, + MRNUMBER = {3748903}, +MRREVIEWER = {Sebasti\'{a}n Reyes-Carocca}, + DOI = {10.1007/978-3-319-68103-0_16}, + URL = {https://doi.org/10.1007/978-3-319-68103-0_16}, +} + +@inproceedings {MR0219507, + AUTHOR = {Birch, B. J.}, + TITLE = {Cyclotomic fields and {K}ummer extensions}, + BOOKTITLE = {Algebraic {N}umber {T}heory ({P}roc. {I}nstructional {C}onf., + {B}righton, 1965)}, + PAGES = {85--93}, + PUBLISHER = {Thompson, Washington, D.C.}, + YEAR = {1967}, + MRCLASS = {10.66}, + MRNUMBER = {0219507}, +MRREVIEWER = {K. Masuda}, +} + +@article {MR891585, + AUTHOR = {Waterhouse, William C.}, + TITLE = {A unified {K}ummer-{A}rtin-{S}chreier sequence}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {277}, + YEAR = {1987}, + NUMBER = {3}, + PAGES = {447--451}, + ISSN = {0025-5831}, + MRCLASS = {14L20 (13B05)}, + MRNUMBER = {891585}, +MRREVIEWER = {Lindsay N. Childs}, + DOI = {10.1007/BF01458325}, + URL = {https://doi.org/10.1007/BF01458325}, +} + +@article {MR593611, + AUTHOR = {Waterhouse, William C. and Weisfeiler, Boris}, + TITLE = {One-dimensional affine group schemes}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {66}, + YEAR = {1980}, + NUMBER = {2}, + PAGES = {550--568}, + ISSN = {0021-8693}, + MRCLASS = {14L15}, + MRNUMBER = {593611}, +MRREVIEWER = {M. Kh. Gizatullin}, + DOI = {10.1016/0021-8693(80)90104-0}, + URL = {https://doi.org/10.1016/0021-8693(80)90104-0}, +} + +@inproceedings {MR1159208, + AUTHOR = {Ihara, Yasutaka}, + TITLE = {Braids, {G}alois groups, and some arithmetic functions}, + BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of + {M}athematicians, {V}ol. {I}, {II} ({K}yoto, 1990)}, + PAGES = {99--120}, + PUBLISHER = {Math. Soc. Japan, Tokyo}, + YEAR = {1991}, + MRCLASS = {11G09 (11R32 14E20 16W30 20F34)}, + MRNUMBER = {1159208}, +MRREVIEWER = {Jerzy Browkin}, +} + +@book {SGA1, + AUTHOR = {Grothendieck, Alexander}, + TITLE = {Rev\^{e}tements \'{e}tales et groupe fondamental. {F}asc. {I}: + {E}xpos\'{e}s 1 \`a 5}, + SERIES = {S\'{e}minaire de G\'{e}om\'{e}trie Alg\'{e}brique}, + VOLUME = {1960/61}, + PUBLISHER = {Institut des Hautes \'{E}tudes Scientifiques, Paris}, + YEAR = {1963}, + PAGES = {iv+143 pp. (not consecutively paged) (loose errata)}, + MRCLASS = {14.55}, + MRNUMBER = {0217087}, +} + +@misc{SGA1a, +Author = {Alexander Grothendieck and Michele Raynaud}, +Title = {Revêtements étales et groupe fondamental (SGA 1)}, +Year = {2002}, +url = {arXiv:math/0206203}, +} + + +@article {MR4037406, + AUTHOR = {Ein, Lawrence and Lazarsfeld, Robert}, + TITLE = {Tangent developable surfaces and the equations defining + algebraic curves}, + JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, + FJOURNAL = {American Mathematical Society. Bulletin. New Series}, + VOLUME = {57}, + YEAR = {2020}, + NUMBER = {1}, + PAGES = {23--38}, + ISSN = {0273-0979}, + MRCLASS = {14H51 (13D02 14N05)}, + MRNUMBER = {4037406}, +MRREVIEWER = {Jos\'{e} Ignacio Farr\'{a}n}, + DOI = {10.1090/bull/1683}, + URL = {https://doi.org/10.1090/bull/1683}, +} + + + +@article {MR4130074, + AUTHOR = {Bleher, Frauke M. and Chinburg, Ted and Kontogeorgis, + Aristides}, + TITLE = {Galois structure of the holomorphic differentials of curves}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {216}, + YEAR = {2020}, + PAGES = {1--68}, + ISSN = {0022-314X}, + MRCLASS = {14G35 (11G20 14G17 14H05 20C20)}, + MRNUMBER = {4130074}, + DOI = {10.1016/j.jnt.2020.04.015}, + URL = {https://doi.org/10.1016/j.jnt.2020.04.015}, +} + +@book {MR2573635, + AUTHOR = {Aprodu, Marian and Nagel, Jan}, + TITLE = {Koszul cohomology and algebraic geometry}, + SERIES = {University Lecture Series}, + VOLUME = {52}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2010}, + PAGES = {viii+125}, + ISBN = {978-0-8218-4964-4}, + MRCLASS = {14H51 (13D02 14C20)}, + MRNUMBER = {2573635}, +MRREVIEWER = {Montserrat Teixidor i Bigas}, + DOI = {10.1090/ulect/052}, + URL = {https://doi.org/10.1090/ulect/052}, +} + +@article {MR1333036, + AUTHOR = {Taylor, Richard and Wiles, Andrew}, + TITLE = {Ring-theoretic properties of certain {H}ecke algebras}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {141}, + YEAR = {1995}, + NUMBER = {3}, + PAGES = {553--572}, + ISSN = {0003-486X}, + MRCLASS = {11G18 (11D41 11F11 11R34 13C40)}, + MRNUMBER = {1333036}, +MRREVIEWER = {Karl Rubin}, + DOI = {10.2307/2118560}, + URL = {https://doi.org/10.2307/2118560}, +} + +@book {MR631688, + AUTHOR = {Zagier, Don B.}, + TITLE = {Zetafunktionen und quadratische {K}\"{o}rper}, + NOTE = {Eine Einf\"{u}hrung in die h\"{o}here Zahlentheorie. [An introduction + to higher number theory], + Hochschultext. [University Text]}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1981}, + PAGES = {viii+144}, + ISBN = {3-540-10603-0}, + MRCLASS = {10-01}, + MRNUMBER = {631688}, +MRREVIEWER = {Matti Jutila}, +} + +@book {MR2849570, + AUTHOR = {M\"{u}ller-Stach, Stefan and Piontkowski, Jens}, + TITLE = {Elementare und algebraische {Z}ahlentheorie}, + EDITION = {Second}, + NOTE = {Ein moderner Zugang zu klassischen Themen. [A modern approach + to classical themes]}, + PUBLISHER = {Vieweg + Teubner, Wiesbaden}, + YEAR = {2011}, + PAGES = {viii+261}, + ISBN = {978-3-8348-1256-8}, + MRCLASS = {11-01}, + MRNUMBER = {2849570}, +MRREVIEWER = {Heinrich Rolletschek}, + DOI = {10.1007/978-3-8348-8263-9}, + URL = {https://doi.org/10.1007/978-3-8348-8263-9}, +} + + +@book {Hunter, + AUTHOR = {Hunter, John }, + TITLE = {Αριθµοθεωρία (µετάφραση Ν. Κρητικού)}, + PUBLISHER = {Σύλλογος προς διάδοσιν ωφελίµων ϐιϐλίων}, + YEAR = {1980}, +} + +@book {Lakis, + AUTHOR = {Λάκκης, Κωσταντίνος }, + TITLE = {Θεωρία Αριθμών}, + PUBLISHER = {Εκδ. Ζήτη}, + YEAR = {1990}, +} + +@book {LakisAlg, + AUTHOR = {Λάκκης, Κωσταντίνος }, + TITLE = {Άλγεβρα}, + PUBLISHER = {Εκδ. Ζήτη}, + YEAR = {1991}, +} + + +@article {MR279069, + AUTHOR = {Williams, Kenneth S.}, + TITLE = {Integers of biquadratic fields}, + JOURNAL = {Canad. Math. Bull.}, + FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de + Math\'{e}matiques}, + VOLUME = {13}, + YEAR = {1970}, + PAGES = {519--526}, + ISSN = {0008-4395}, + MRCLASS = {10.66}, + MRNUMBER = {279069}, +MRREVIEWER = {W. J. Ellison}, + DOI = {10.4153/CMB-1970-094-8}, +} + +@book {MR2031707, + AUTHOR = {Alaca, \c{S}aban and Williams, Kenneth S.}, + TITLE = {Introductory {A}lgebraic {N}umber {T}heory}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2004}, + PAGES = {xviii+428}, + ISBN = {0-521; 0-521-54011-9}, + MRCLASS = {11Rxx (11-01)}, + MRNUMBER = {2031707}, +MRREVIEWER = {Charles J. Parry}, +} + +@book {MR1215934, + AUTHOR = {Fr\"{o}hlich, Albrecht and Taylor, J. Martin}, + TITLE = {Algebraic number theory}, + SERIES = {Cambridge Studies in advanced mathematics}, + VOLUME = {27}, + PUBLISHER = {Cambridge: Cambridge University Press}, + YEAR = {1993}, + PAGES = {xiv+355}, + ISBN = {0-521-43834-9}, + MRCLASS = {11Rxx (13F05)}, + MRNUMBER = {1215934}, +MRREVIEWER = {Jerzy Browkin}, +} + +@book {MR1362545, + AUTHOR = {Janusz, Gerald J.}, + TITLE = {Algebraic {N}umber {F}ields}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {7}, + EDITION = {2nd edition}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1996}, + PAGES = {x+276}, + ISBN = {0-8218-0429-4}, + MRCLASS = {11Rxx (11-02 11R37)}, + MRNUMBER = {1362545}, +MRREVIEWER = {W. Narkiewicz}, + DOI = {10.1090/gsm/007}, +} + +@book {MR2078267, + AUTHOR = {Narkiewicz, W\l adys\l aw}, + TITLE = {Elementary and {A}nalytic {T}heory of {A}lgebraic {N}umbers}, + SERIES = {Springer Monographs in Mathematics}, + EDITION = {3rd edition}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2004}, + PAGES = {xii+708}, + ISBN = {3-540-21902-1}, + MRCLASS = {11Rxx (11-01 11-02)}, + MRNUMBER = {2078267}, + DOI = {10.1007/978-3-662-07001-7}, +} + +@book {MR0265266, + AUTHOR = {Samuel, Pierre}, + TITLE = {Algebraic {T}heory of {N}umbers}, + SERIES = {Translated from the French by Allan J. Silberger}, + PUBLISHER = {Houghton Mifflin Co., Boston, Mass.}, + YEAR = {1970}, + PAGES = {109}, + MRCLASS = {10.01}, + MRNUMBER = {0265266}, +} + +@book {MR3236783, + AUTHOR = {Cox, David A.}, + TITLE = {Primes of the {F}orm {$x^2 + ny^2$}, + Fermat, class field theory, and complex multiplication}, + SERIES = {Pure and Applied Mathematics}, + EDITION = {2nd edition}, + PUBLISHER = {John Wiley \& Sons, Inc.}, + YEAR = {2013}, + PAGES = {xviii+356}, + ISBN = {978-1-118-39018-4}, + MRCLASS = {11A41 (11F11 11R11 11R16 11R18 11R37 11Y11)}, + MRNUMBER = {3236783}, +MRREVIEWER = {Michael C. Berg}, + DOI = {10.1002/9781118400722}, +} + + +@book {MR0197380, + AUTHOR = {Gauss, Carl Friedrich}, + TITLE = {Disquisitiones {A}rithmeticae}, + SERIES = {Translated into English by Arthur A. Clarke, S. J}, + PUBLISHER = {Yale University Press, New Haven, Conn.-London}, + YEAR = {1966}, + PAGES = {xx+472}, + MRCLASS = {10.00 (01.60)}, + MRNUMBER = {0197380}, +MRREVIEWER = {W. J. LeVeque}, +} + + +@book {MR2303999, + AUTHOR = {Weil, Andr\'{e}}, + TITLE = {Number {T}heory, An approach through history from Hammurapi to Legendre, + Reprint of the 1984 edition}, + SERIES = {Modern Birkh\"{a}user Classics}, + PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA}, + YEAR = {2007}, + PAGES = {xxii+377}, + ISBN = {978-0-8176-4565-6; 0-8176-4565-9}, + MRCLASS = {01A05 (01A75 11-01)}, + MRNUMBER = {2303999}, + } + + +@book {MR1384299, + AUTHOR = {Redmond, Don}, + TITLE = {Number {T}heory, An introduction}, + SERIES = {Monographs and Textbooks in Pure and Applied Mathematics}, + VOLUME = {201}, + PUBLISHER = {Marcel Dekker, Inc., New York}, + YEAR = {1996}, + PAGES = {xiv+749}, + ISBN = {0-8247-9696-9}, + MRCLASS = {11-01}, + MRNUMBER = {1384299}, +MRREVIEWER = {Joe P. Buhler}, +} + + +@book {MR1486041, + AUTHOR = {Goldman, Jay R.}, + TITLE = {The {Q}ueen of {M}athematics, + A historically motivated guide to {N}umber {T}heory}, + PUBLISHER = {A K Peters, Ltd., Wellesley, MA}, + YEAR = {1998}, + PAGES = {xxiv+525}, + ISBN = {1-56881-006-7}, + MRCLASS = {11-01 (11-03)}, + MRNUMBER = {1486041}, +MRREVIEWER = {M. Ram Murty}, +} + +@book {MR1083765, + AUTHOR = {Niven, Ivan and Zuckerman, Herbert S. and Montgomery, Hugh L.}, + TITLE = {An {I}ntroduction to the {T}heory of {N}umbers}, + EDITION = {Fifth}, + PUBLISHER = {John Wiley \& Sons, Inc., New York}, + YEAR = {1991}, + PAGES = {xiv+529}, + ISBN = {0-471-62546-9}, + MRCLASS = {11-01}, + MRNUMBER = {1083765}, +} + + +@book {MR770936, + AUTHOR = {Scharlau, Winfried and Opolka, Hans}, + TITLE = {From {F}ermat to {M}inkowski}, + SERIES = {Undergraduate Texts in Mathematics}, + NOTE = {Lectures on the theory of numbers and its historical + development, + Translated from the German by Walter K. B\"{u}hler and Gary + Cornell}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1985}, + PAGES = {xi+184}, + ISBN = {0-387-90942-7}, + MRCLASS = {11-03 (01A05 11-01)}, + MRNUMBER = {770936}, + DOI = {10.1007/978-1-4757-1867-6}, + URL = {https://doi.org/10.1007/978-1-4757-1867-6}, +} + +@book {MR0188128, + AUTHOR = {Hasse, Helmut}, + TITLE = {Vorlesungen \"{u}ber {Z}ahlentheorie}, + SERIES = {Zweite neubearbeitete Auflage. Die Grundlehren der + Mathematischen Wissenschaften, Band 59}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1964}, + PAGES = {xv+504}, + MRCLASS = {10.00}, + MRNUMBER = {0188128}, +MRREVIEWER = {G. J. Rieger}, +} + + +@book {MR0476613, + AUTHOR = {Adams, William W. and Goldstein, Larry Joel}, + TITLE = {Introduction to {N}umber {T}heory}, + PUBLISHER = {Prentice-Hall, Inc., Englewood Cliffs, N.J.}, + YEAR = {1976}, + PAGES = {xiii+362}, + MRCLASS = {10-01}, + MRNUMBER = {0476613}, +MRREVIEWER = {Harvey Cohn}, +} + +@book {MR3675899, + AUTHOR = {Pollack, Paul}, + TITLE = {A {C}onversational {I}ntroduction to {A}lgebraic {N}umber {T}heory, + Arithmetic beyond $\Bbb{Z}$}, + SERIES = {Student Mathematical Library}, + VOLUME = {84}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2017}, + PAGES = {ix + 316}, + ISBN = {978-1-4704-3653-7}, + MRCLASS = {11-01 (11R04 11R11 11R27 11R29 11R32)}, + MRNUMBER = {3675899}, +MRREVIEWER = {Charles Helou}, + DOI = {10.1090/stml/084}, +} + +@book {MR3086176, + AUTHOR = {Halter-Koch, Franz}, + TITLE = {Quadratic {I}rrationals, An {I}ntroduction to {C}lassical {N}umber {T}heory}, + SERIES = {Pure and Applied Mathematics (Boca Raton)}, + PUBLISHER = {CRC Press, Boca Raton, FL}, + YEAR = {2013}, + PAGES = {xvi+415}, + ISBN = {978-1-4665-9183-7}, + MRCLASS = {11-01 (11A25 11Lxx 11Mxx 11N37 11R11)}, + MRNUMBER = {3086176}, +MRREVIEWER = {Olivier Bordell\`es}, + DOI = {10.1201/b14968}, + URL = {https://doi.org/10.1201/b14968}, +} + +@book {MR551363, + AUTHOR = {Ribenboim, Paulo}, + TITLE = {13 lectures on {F}ermat's last theorem}, + PUBLISHER = {Springer-Verlag, New York-Heidelberg}, + YEAR = {1979}, + PAGES = {xvi+302 pp. (1 plate)}, + ISBN = {0-387-90432-8}, + MRCLASS = {10B15 (01A55 12A35 12A65)}, + MRNUMBER = {551363}, +MRREVIEWER = {T. Mets\"{a}nkyl\"{a}}, +} + + +@book {MR0195803, + AUTHOR = {Borevich, Zenon and Shafarevich, R. Igor}, + TITLE = {Number theory}, + SERIES = {Translated from the Russian by Newcomb Greenleaf. Pure and + Applied Mathematics, Vol. 20}, + PUBLISHER = {Academic Press, New York-London}, + YEAR = {1966}, + PAGES = {x+435}, + MRCLASS = {10.00}, + MRNUMBER = {0195803}, +} + +@book {MR1421575, + AUTHOR = {Washington, Lawrence C.}, + TITLE = {Introduction to {C}yclotomic {F}ields}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {83}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1997}, + PAGES = {xiv+487}, + ISBN = {0-387-94762-0}, + MRCLASS = {11R18 (11-01 11-02 11R23)}, + MRNUMBER = {1421575}, +MRREVIEWER = {T. Mets\"{a}nkyl\"{a}}, + DOI = {10.1007/978-1-4612-1934-7}, + URL = {https://doi.org/10.1007/978-1-4612-1934-7}, +} + +@book {MR3822326, + AUTHOR = {Marcus, Daniel A.}, + TITLE = {Algebraic {N}umber {F}ields}, + SERIES = {Universitext}, + NOTE = {2nd edition of [ MR0457396], + With a foreword by Barry Mazur}, + PUBLISHER = {Springer}, + YEAR = {2018}, + PAGES = {xviii+203}, + ISBN = {978-3-319-90232-6; 978-3-319-90233-3}, + MRCLASS = {11-01 (11Rxx 11Txx 12-01)}, + MRNUMBER = {3822326}, + DOI = {10.1007/978-3-319-90233-3}, +} + +@book{lemmermeyer2017quadratische, + title={Quadratische {Z}ahlk{\"o}rper: {E}ine {E}inf{\"u}hrung mit vielen {B}eispielen}, + author={Lemmermeyer, Franz}, + isbn={9783662538227}, + url={https://books.google.gr/books?id=z5ErDwAAQBAJ}, + year={2017}, + publisher={Springer Berlin} +} + +@ARTICLE{Hilgert2018-zr, + title = "Franz {L}emmermeyer: {Q}uadratische {Z}ahlk{\"o}rper -- Eine + {E}inf{\"u}hrung mit vielen {B}eispielen", + author = "Hilgert, Joachim", + journal = "Math. Semesterber.", + volume = 65, + number = 1, + pages = "129--131", + month = mar, + year = 2018, + url = "https://doi.org/10.1007/s00591-018-0218-7", + issn = "0720-728X, 1432-1815", + doi = "10.1007/s00591-018-0218-7" +} + +@article {MR961918, + AUTHOR = {Silverman, Joseph H.}, + TITLE = {Wieferich's criterion and the {$abc$}-conjecture}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {30}, + YEAR = {1988}, + NUMBER = {2}, + PAGES = {226--237}, + ISSN = {0022-314X}, + MRCLASS = {11D41 (11G05)}, + MRNUMBER = {961918}, +MRREVIEWER = {Daniel Bertrand}, + DOI = {10.1016/0022-314X(88)90019-4}, +} + +@article {MR3659215, + AUTHOR = {Gassert, T. Alden}, + TITLE = {A note on the monogeneity of power maps}, + JOURNAL = {Albanian J. Math.}, + FJOURNAL = {Albanian Journal of Mathematics}, + VOLUME = {11}, + YEAR = {2017}, + NUMBER = {1}, + PAGES = {3--12}, + MRCLASS = {11R09 (11R04)}, + MRNUMBER = {3659215}, +MRREVIEWER = {K. Gy\H{o}ry}, +} + +@article {MR687621, + AUTHOR = {Llorente, Pascual and Nart, Enric}, + TITLE = {Effective determination of the decomposition of the rational + primes in a cubic field}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {87}, + YEAR = {1983}, + NUMBER = {4}, + PAGES = {579--585}, + ISSN = {0002-9939}, + MRCLASS = {12A30 (12A50)}, + MRNUMBER = {687621}, +MRREVIEWER = {Richard Massy}, + DOI = {10.2307/2043339}, +} + +@article {MR1459102, + AUTHOR = {Alaca, \c{S}aban}, + TITLE = {{$p$}-integral bases of a cubic field}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {126}, + YEAR = {1998}, + NUMBER = {7}, + PAGES = {1949--1953}, + ISSN = {0002-9939}, + MRCLASS = {11R16}, + MRNUMBER = {1459102}, +MRREVIEWER = {Enric Nart}, + DOI = {10.1090/S0002-9939-98-04422-0}, +} + +@book {MR0184933, + AUTHOR = {Berwick, W. E. H.}, + TITLE = {Integral {B}ases}, + SERIES = {Cambridge Tracts in Mathematics and Mathematical Physics, No. + 22}, + PUBLISHER = {Stechert-Hafner, Inc., New York}, + YEAR = {1964}, + PAGES = {v+95}, + MRCLASS = {12.00}, + MRNUMBER = {0184933}, +} + +@book {MR1228206, + AUTHOR = {Cohen, Henri}, + TITLE = {A {C}ourse in {C}omputational {A}lgebraic {N}umber {T}heory}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {138}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1993}, + PAGES = {xii+534}, + ISBN = {3-540-55640-0}, + MRCLASS = {11Y40 (11Rxx 68Q40)}, + MRNUMBER = {1228206}, +MRREVIEWER = {Joe P. Buhler}, + DOI = {10.1007/978-3-662-02945-9}, +} + +@book {MR3970246, + AUTHOR = {Ga\'{a}l, Istv\'{a}n}, + TITLE = {Diophantine {E}quations and {P}ower {I}ntegral {B}ases}, + NOTE = {Theory and algorithms, + Second edition of [ MR1896601]}, + PUBLISHER = {Birkh\"{a}user/Springer, Cham}, + YEAR = {2019}, + PAGES = {xxii+326}, + ISBN = {978-3-030-23864-3; 978-3-030-23865-0}, + MRCLASS = {11D57 (11D59 11R04 11R33 11Y50)}, + MRNUMBER = {3970246}, +MRREVIEWER = {Yann Bugeaud}, + DOI = {10.1007/978-3-030-23865-0}, +} + + +@phdthesis{MotodaPhd, + author = {Motoda, Yasuo}, + title = {On Power {I}ntegral {B}ases for {C}ertain {A}belian {F}ields}, + school = {}, + year = {2011}, + +} + +@misc{milneANT, +author={Milne, James S.}, +title={Algebraic {N}umber {T}heory (v3.08)}, +year={2020}, +note={Available at www.jmilne.org/math/}, +pages={166} +} + + +@ARTICLE{Stein2012-qz, + title = "Algebraic {N}umber {T}heory, a computational approach", + author = "Stein, William", + journal = "Harvard. Massachusetts", + year = 2012, + url = "https://wstein.org/books/ant/ant.pdf" +} + + +@book {MR1712469, + AUTHOR = {Migliore, Juan C.}, + TITLE = {Introduction to liaison theory and deficiency modules}, + SERIES = {Progress in Mathematics}, + VOLUME = {165}, + PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA}, + YEAR = {1998}, + PAGES = {xiv+215}, + ISBN = {0-8176-4027-4}, + MRCLASS = {14M06 (13C40 13D45 14F05)}, + MRNUMBER = {1712469}, +MRREVIEWER = {Martin Kreuzer}, + DOI = {10.1007/978-1-4612-1794-7}, + URL = {https://doi.org/10.1007/978-1-4612-1794-7}, +} + +@article{1604.07746, +Author = {Sander G. Huisman}, +Title = {Newer sums of three cubes}, +Year = {2016}, +url = {arXiv:1604.07746}, +} + +@article{HKochJahr, +Author ={Helmut Koch}, +title ={Jahresbericht der {DMV}}, +volume= {89}, +number= {3}, +year={1987}, +note={σελ. 32} +} + +@book {DummitFoote, + AUTHOR = {Dummit, David S. and Foote, Richard M.}, + TITLE = {Abstract {A}lgebra}, + EDITION = {3rd edition}, + PUBLISHER = {John Wiley \& Sons, Inc., Hoboken, NJ}, + YEAR = {2004}, + PAGES = {xii+932}, + ISBN = {0-471-43334-9}, + MRCLASS = {00-01 (16-01 20-01)}, + MRNUMBER = {2286236}, +} + +@book{schulenberger2003algebra, + title={Algebra}, + author={Schulenberger, J.R. and van der Waerden, B.L.}, + number={$\tau$. 2}, + isbn={9780387406251}, + url={https://books.google.gr/books?id=cvOgYpQ7KMIC}, + year={2003}, + publisher={Springer New York} +} + +@book{bosch2013algebra, + title={Algebra}, + author={Bosch, Siegfried}, + isbn={9783662056493}, + series={Springer-Lehrbuch}, + url={https://books.google.gr/books?id=4BiyBgAAQBAJ}, + year={2013}, + publisher={Springer Berlin} +} + +@article {MR288094, + AUTHOR = {MacKenzie, Robert and Scheuneman, John}, + TITLE = {A number field without a relative integral basis}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {78}, + YEAR = {1971}, + PAGES = {882--883}, + ISSN = {0002-9890}, + MRCLASS = {10.65}, + MRNUMBER = {288094}, +MRREVIEWER = {Stephen I. Gendler}, + DOI = {10.2307/2316485}, +} + +@book {MR1821363, + AUTHOR = {Ribenboim, Paulo}, + TITLE = {Classical {T}heory of {A}lgebraic {N}umbers}, + SERIES = {Universitext}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2001}, + PAGES = {xxiv+681}, + ISBN = {0-387-95070-2}, + MRCLASS = {11-01 (11Rxx)}, + MRNUMBER = {1821363}, +MRREVIEWER = {Lawrence Washington}, + DOI = {10.1007/978-0-387-21690-4}, +} + +@MastersThesis{Anthi, + author = {Anthi Zervou}, + title = {Profinite {G}roups and {C}ohomology}, + school = {Πανεπιστήμιο Κρήτης}, + year = {2017}, + +} + + +@book {MR0220700, + AUTHOR = {Hasse, Helmut}, + TITLE = {Vorlesungen \"{u}ber {K}lassenk\"{o}rpertheorie}, + SERIES = {Thesaurus Mathematicae, Band 6}, + PUBLISHER = {Physica-Verlag, W\"{u}rzburg}, + YEAR = {1967}, + PAGES = {iii+275}, + MRCLASS = {10.68}, + MRNUMBER = {0220700}, +MRREVIEWER = {O. F. G. Schilling}, +} + +@book{leutbecher2013zahlentheorie, + title={Zahlentheorie: Eine Einf{\"u}hrung in die Algebra}, + author={Leutbecher, A.}, + isbn={9783642614057}, + series={Springer-Lehrbuch}, + url={https://books.google.gr/books?id=PG2nBgAAQBAJ}, + year={2013}, + publisher={Springer, Berlin} +} + +@book {MR1070716, + AUTHOR = {Ireland, Kenneth and Rosen, Michael}, + TITLE = {A classical {I}ntroduction to {M}odern {N}umber {T}heory}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {84}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1990}, + PAGES = {xiv+389}, + ISBN = {0-387-97329-X}, + MRCLASS = {11-01 (11-02)}, + MRNUMBER = {1070716}, +MRREVIEWER = {Glenn Stevens}, + DOI = {10.1007/978-1-4757-2103-4}, + } + + +@book {MR0253972, + AUTHOR = {Hasse, Helmut}, + TITLE = {Zahlentheorie}, + SERIES = {Dritte berichtigte Auflage}, + PUBLISHER = {Akademie-Verlag, Berlin}, + YEAR = {1969}, + PAGES = {xvi+611}, + MRCLASS = {10.00}, + MRNUMBER = {0253972}, +} + +@book {MR3561102, + AUTHOR = {Hiramatsu, Toyokazu and Saito, Seiken}, + TITLE = {An {I}ntroduction to non-abelian {C}lass {F}ield {T}heory}, + SERIES = {Series on Number Theory and its Applications}, + VOLUME = {13}, + NOTE = {Automorphic forms of weight 1 and 2-dimensional Galois + representations}, + PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, + YEAR = {2017}, + PAGES = {xii+175}, + ISBN = {978-981-3142-26-8}, + MRCLASS = {11-02 (11Fxx)}, + MRNUMBER = {3561102}, +MRREVIEWER = {Stefan K\"{u}hnlein}, +} + +@book {MR1434478, + AUTHOR = {Cassels, J. W. S.}, + TITLE = {An {I}ntroduction to the {G}eometry of {N}umbers}, + SERIES = {Classics in Mathematics}, + NOTE = {Corrected reprint of the 1971 edition}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1997}, + PAGES = {viii+344}, + ISBN = {3-540-61788-4}, + MRCLASS = {11Hxx}, + MRNUMBER = {1434478}, +} + +@book {MR0282947, + AUTHOR = {Lang, Serge}, + TITLE = {Algebraic {N}umber {T}heory}, + PUBLISHER = {Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don + Mills, Ont.}, + YEAR = {1970}, + PAGES = {xi+354}, + MRCLASS = {10.68}, + MRNUMBER = {0282947}, +MRREVIEWER = {G. Whaples}, +} + +@book {MR0132037, + AUTHOR = {Artin, Emil}, + TITLE = {Theory of {A}lgebraic {N}umbers}, + SERIES = {Notes by Gerhard W\"{u}rges from lectures held at the + Mathematisches Institut, G\"{o}ttingen, Germany, in the Winter + Semester}, + VOLUME = {1956/7}, + PUBLISHER = {George Striker, Schildweg 12, G\"{o}ttingen}, + YEAR = {1959}, + PAGES = {172}, + MRCLASS = {10.65}, + MRNUMBER = {0132037}, +MRREVIEWER = {L. Carlitz}, +} + +@misc{Conrad-Dirichlet, + author = "Keith Conrad", + title = "Dirichlet's Unit Theorem", + url = "https://home.mathematik.uni-freiburg.de/arithgeom/lehre/ss20/algzt/Keith%20Conrad%20-%20Unit%20theorem.pdf" +} + +@misc{Conrad-PID, + author = "Keith Conrad", + title = "Finitely Generated Modules over a PID", + note = "URL: \url{http://math.stanford.edu/~conrad/210APage/handouts/PIDGreg.pdf +}" +} + +@misc{Conrad-diff, + author = "Keith Conrad", + title = "The different ideal", + note = "URL: \url{https://kconrad.math.uconn.edu/blurbs/gradnumthy/different.pdf +}" +} + + +@book {MR1483321, + AUTHOR = {Pohst, M. and Zassenhaus, H.}, + TITLE = {Algorithmic {A}lgebraic {N}umber {T}heory}, + SERIES = {Encyclopedia of Mathematics and its Applications}, + VOLUME = {30}, + NOTE = {Revised reprint of the 1989 original}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1997}, + PAGES = {xiv+499}, + ISBN = {0-521-59669-6}, + MRCLASS = {11Rxx (11Y40)}, + MRNUMBER = {1483321}, +} + +@article {MR32592, + AUTHOR = {Motzkin, Th.}, + TITLE = {The {E}uclidean algorithm}, + JOURNAL = {Bull. Amer. Math. Soc.}, + FJOURNAL = {Bulletin of the American Mathematical Society}, + VOLUME = {55}, + YEAR = {1949}, + PAGES = {1142--1146}, + ISSN = {0002-9904}, + MRCLASS = {09.1X}, + MRNUMBER = {32592}, +MRREVIEWER = {B. N. Moyls}, + DOI = {10.1090/S0002-9904-1949-09344-8}, + URL = {https://doi.org/10.1090/S0002-9904-1949-09344-8}, +} + +@article {MR41885, + AUTHOR = {Chatland, H. and Davenport, H.}, + TITLE = {Euclid's algorithm in real quadratic fields}, + JOURNAL = {Canad. J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {2}, + YEAR = {1950}, + PAGES = {289--296}, + ISSN = {0008-414X}, + MRCLASS = {10.0X}, + MRNUMBER = {41885}, +MRREVIEWER = {L. Schoenfeld}, + DOI = {10.4153/cjm-1950-026-7}, + URL = {https://doi.org/10.4153/cjm-1950-026-7}, +} + +@article {MR1277533, + AUTHOR = {Clark, David A.}, + TITLE = {A quadratic field which is {E}uclidean but not + norm-{E}uclidean}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {83}, + YEAR = {1994}, + NUMBER = {3-4}, + PAGES = {327--330}, + ISSN = {0025-2611}, + MRCLASS = {11R11 (13F07)}, + MRNUMBER = {1277533}, +MRREVIEWER = {Amara H\'{e}di}, + DOI = {10.1007/BF02567617}, + URL = {https://doi.org/10.1007/BF02567617}, +} + +@article {MR2363830, + AUTHOR = {Narkiewicz, W\l adys\l aw}, + TITLE = {Euclidean {A}lgorithm in small abelian fields}, + JOURNAL = {Funct. Approx. Comment. Math.}, + FJOURNAL = {Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydzia\l + Matematyki i Informatyki. Functiones et Approximatio + Commentarii Mathematici}, + VOLUME = {37}, + YEAR = {2007}, + NUMBER = {part 2}, + PAGES = {337--340}, + ISSN = {0208-6573}, + MRCLASS = {11R11 (11R20 11R47)}, + MRNUMBER = {2363830}, +MRREVIEWER = {Kunpeng Wang}, + DOI = {10.7169/facm/1229619657}, + URL = {https://doi.org/10.7169/facm/1229619657}, +} + +@article {MR280470, + AUTHOR = {Samuel, Pierre}, + TITLE = {About {E}uclidean rings}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {19}, + YEAR = {1971}, + PAGES = {282--301}, + ISSN = {0021-8693}, + MRCLASS = {13.15 (14.00)}, + MRNUMBER = {280470}, +MRREVIEWER = {R. M. Fossum}, + DOI = {10.1016/0021-8693(71)90110-4}, + URL = {https://doi.org/10.1016/0021-8693(71)90110-4}, +} + +@phdthesis{phdHarper, + author = {H. Harper}, + title = {{$\Bbb Z[\sqrt{14}]$} is {E}uclidean}, + school = {Mc Gill Montreal Canada}, + year = 2000, +} + +@article {MR2031122, + AUTHOR = {Harper, Malcolm}, + TITLE = {{$\Bbb Z[\sqrt{14}]$} is {E}uclidean}, + JOURNAL = {Canad. J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {56}, + YEAR = {2004}, + NUMBER = {1}, + PAGES = {55--70}, + ISSN = {0008-414X}, + MRCLASS = {11R04 (11R11)}, + MRNUMBER = {2031122}, +MRREVIEWER = {V. Kumar Murty}, + DOI = {10.4153/CJM-2004-003-9}, + URL = {https://doi.org/10.4153/CJM-2004-003-9}, +} + +@book {MR0345993, + AUTHOR = {Adamson, Iain T.}, + TITLE = {Elementary {R}ings and {M}odules}, + NOTE = {University Mathematical Texts}, + PUBLISHER = {Barnes \& Noble Books [A division of Harper \& Row, + Publishers, Inc.], New York; Oliver and Boyd, + Edinburgh-London}, + YEAR = {1972}, + PAGES = {vi+136}, + MRCLASS = {16-01 (13-01)}, + MRNUMBER = {0345993}, +} + +@book {MR619212, + AUTHOR = {Hartley, B. and Hawkes, T. O.}, + TITLE = {Rings, modules and linear algebra}, + PUBLISHER = {Chapman \& Hall, London-New York}, + YEAR = {1980}, + PAGES = {xi+210}, + ISBN = {0-412-09810-5}, + MRCLASS = {00A05 (16-01)}, + MRNUMBER = {619212}, +} + +@book {AlgebraVar, + AUTHOR = {Δ. Βάρσος and Δ. Δεριζιώτης and Ι. Εμμανουλ and Ο. Ταλλέλη }, + TITLE = {Μια εισαγωγή στην Άλγεβρα}, + PUBLISHER = {Εκδ. Σοφία}, + YEAR = {2012}, +} + +@book {AlgebraFra, + AUTHOR = {John Fraleigh }, + TITLE = {Eισαγωγή στην Άλγεβρα}, + PUBLISHER = {Πανεπιστημιακές Εκδόσεις Κρήτης}, + YEAR = {2015}, +} + +@book {MR1714917, + AUTHOR = {Ueno, Kenji}, + TITLE = {Algebraic geometry. 1}, + SERIES = {Translations of Mathematical Monographs}, + VOLUME = {185}, + NOTE = {From algebraic varieties to schemes, + Translated from the 1997 Japanese original by Goro Kato, + Iwanami Series in Modern Mathematics}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1999}, + PAGES = {xx+154}, + ISBN = {0-8218-0862-1}, + MRCLASS = {14-01 (14A10 14A15)}, + MRNUMBER = {1714917}, +MRREVIEWER = {Reinhold H\"{u}bl}, + DOI = {10.1090/mmono/185}, + URL = {https://doi.org/10.1090/mmono/185}, +} + +@book {MR575344, + AUTHOR = {Matsumura, Hideyuki}, + TITLE = {Commutative algebra}, + SERIES = {Mathematics Lecture Note Series}, + VOLUME = {56}, + EDITION = {Second}, + PUBLISHER = {Benjamin/Cummings Publishing Co., Inc., Reading, Mass.}, + YEAR = {1980}, + PAGES = {xv+313}, + ISBN = {0-8053-7026-9}, + MRCLASS = {13-02}, + MRNUMBER = {575344}, +MRREVIEWER = {R. M. Fossum}, +} + +@article {MR218328, + AUTHOR = {Neukirch, J\"{u}rgen}, + TITLE = {Zur {D}ifferententheorie}, + JOURNAL = {Arch. Math. (Basel)}, + FJOURNAL = {Archiv der Mathematik}, + VOLUME = {18}, + YEAR = {1967}, + PAGES = {241--249}, + ISSN = {0003-889X}, + MRCLASS = {10.65}, + MRNUMBER = {218328}, +MRREVIEWER = {T. Kubota}, + DOI = {10.1007/BF01900629}, + URL = {https://doi.org/10.1007/BF01900629}, +} + +@article {MR238817, + AUTHOR = {Narkiewicz, W.}, + TITLE = {On a theorem of {A}. {W}eil on derivations in number fields}, + JOURNAL = {Colloq. Math.}, + FJOURNAL = {Colloquium Mathematicum}, + VOLUME = {20}, + YEAR = {1969}, + PAGES = {57--58}, + ISSN = {0010-1354}, + MRCLASS = {12.50}, + MRNUMBER = {238817}, +MRREVIEWER = {T. Kubota}, + DOI = {10.4064/cm-20-1-57-58}, + URL = {https://doi.org/10.4064/cm-20-1-57-58}, +} + + +@article {WeilDiff, + AUTHOR = {Weil, A.}, + TITLE = {Differentiation in algebraic number fields}, + JOURNAL = {Bulletin of the AMS}, + FJOURNAL = {Bulletin of the AMS}, + VOLUME = {49}, + YEAR = {1943}, + PAGES = {41}, +} + +@incollection {MR0049233, + AUTHOR = {\v{S}afarevi\v{c}, I. R.}, + TITLE = {A new proof of the {K}ronecker-{W}eber theorem}, + BOOKTITLE = {Trudy {M}at. {I}nst. {S}teklov., v. 38}, + SERIES = {Trudy Mat. Inst. Steklov., v. 38}, + PAGES = {382--387}, + PUBLISHER = {Izdat. Akad. Nauk SSSR, Moscow}, + YEAR = {1951}, + MRCLASS = {10.0X}, + MRNUMBER = {0049233}, +MRREVIEWER = {W. H. Mills}, +} + +@mastersthesis{Kwstantia, + author = {Κωστάντια Μανούσου-Σωτηροποούλου}, + title = {To Θεώρημα {K}ronecker-{W}eber}, + url ={http://users.math.uoc.gr/~antoniad/kronecker_weber.pdf}, + school = {Πανεπιστήμιο Κρήτης}, + year = {2014}, +} + +@mastersthesis{RomainWeber, + author = {Romain Branchereau}, + title = {The {K}ronecker-{W}eber Theorem}, + url ={https://people.math.ethz.ch/~pink/Theses/2016-Bachelor-Romain-Branchereau.pdf}, + school = {ETH, Z\"urich}, + year = {2016}, +} + + + +@book{baggett2011exposition, + title={An Exposition on the Kronecker-Weber Theorem}, + author={Baggett, J.A.}, + url={https://books.google.gr/books?id=nbF7twAACAAJ}, + year={2011}, + publisher={University of Alaska Fairbanks} +} + + + +@article {MR2211307, + AUTHOR = {Lemmermeyer, Franz}, + TITLE = {Kronecker-{W}eber via {S}tickelberger}, + JOURNAL = {J. Th\'{e}or. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'{e}orie des Nombres de Bordeaux}, + VOLUME = {17}, + YEAR = {2005}, + NUMBER = {2}, + PAGES = {555--558}, + ISSN = {1246-7405}, + MRCLASS = {11R18}, + MRNUMBER = {2211307}, +MRREVIEWER = {Robert G. Underwood}, + URL = {http://jtnb.cedram.org/item?id=JTNB_2005__17_2_555_0}, +} + +@book{deuring1966klassenkörpertheorie, + title={Klassenk{\"o}rpertheorie: Vorlesung gehalten im Sommersemester 1965 und Wintersemester 1965-66 in G{\"o}ttingen}, + author={Deuring, M.}, + number={$\tau$. 1}, + url={https://books.google.gr/books?id=CKPNxgEACAAJ}, + year={1966} +} + +@book {MR1646901, + AUTHOR = {Hilbert, David}, + TITLE = {The {T}heory of {A}lgebraic {N}umber {F}ields}, + NOTE = {Translated from the German and with a preface by Iain T. + Adamson, + With an introduction by Franz Lemmermeyer and Norbert + Schappacher}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1998}, + PAGES = {xxxvi+350}, + ISBN = {3-540-62779-0}, + MRCLASS = {01A75 (01A60 11Rxx)}, + MRNUMBER = {1646901}, +MRREVIEWER = {T. Mets\"{a}nkyl\"{a}}, + DOI = {10.1007/978-3-662-03545-0}, + URL = {https://doi.org/10.1007/978-3-662-03545-0}, +} + +@book {MR0124256, + AUTHOR = {Holzer, Ludwig}, + TITLE = {Zahlentheorie. {II}}, + SERIES = {Mathematisch-Naturwissenschaftliche Bibliothek, Bd. 14}, + PUBLISHER = {B. G. Teubner Verlagsgesellschaft, Leipzig}, + YEAR = {1959}, + PAGES = {v+127}, + MRCLASS = {10.01}, + MRNUMBER = {0124256}, +MRREVIEWER = {A. Aigner}, +} + +@book {MR0072174, + AUTHOR = {Mann, Henry B.}, + TITLE = {Introduction to {A}lgebraic {N}umber {T}heory}, + NOTE = {With a chapter by Marshall Hall, Jr.}, + PUBLISHER = {The Ohio State University Press, Columbus, Ohio}, + YEAR = {1955}, + PAGES = {vii+168}, + MRCLASS = {10.2X}, + MRNUMBER = {0072174}, +MRREVIEWER = {K. Iwasawa}, +} + + +@book{theory1997modular, + title={Modular {F}orms and {F}ermat’s {L}ast {T}heorem}, + author={Cornell, Gary and Silverman Joseph and Stevens Glenn}, + isbn={9780387946092}, + lccn={97010930}, + url={https://books.google.gr/books?id=Va-quzVwtMsC}, + year={1997}, + publisher={Springer New York} +} + + +@incollection {MR1638493, + AUTHOR = {Rosen, Michael}, + TITLE = {Remarks on the history of {F}ermat's last theorem 1844 to + 1984}, + BOOKTITLE = {Modular {F}orms and {F}ermat's {L}ast {T}heorem ({B}oston, {MA}, + 1995)}, + PAGES = {505--525}, + PUBLISHER = {Springer, New York}, + YEAR = {1997}, + MRCLASS = {11-03 (01A55 01A60 11D41)}, + MRNUMBER = {1638493}, +} + +@incollection {MR1605752, + AUTHOR = {Darmon, Henri and Diamond, Fred and Taylor, Richard}, + TITLE = {Fermat's {L}ast {T}heorem}, + BOOKTITLE = {Elliptic curves, modular forms \& {F}ermat's last theorem + ({H}ong {K}ong, 1993)}, + PAGES = {2--140}, + PUBLISHER = {Int. Press, Cambridge, MA}, + YEAR = {1997}, + MRCLASS = {11G18 (11D41 11F80 11G05)}, + MRNUMBER = {1605752}, +MRREVIEWER = {M. Ram Murty}, +} + + +@incollection {MR1474977, + AUTHOR = {Darmon, Henri and Diamond, Fred and Taylor, Richard}, + TITLE = {Fermat's {L}ast {T}heorem}, + BOOKTITLE = {Current developments in mathematics, 1995 ({C}ambridge, {MA})}, + PAGES = {1--154}, + PUBLISHER = {Int. Press, Cambridge, MA}, + YEAR = {1994}, + MRCLASS = {11G18 (11D41 11F80 11G05)}, + MRNUMBER = {1474977}, +MRREVIEWER = {M. Ram Murty}, +} + + +@incollection {MR1806208, + AUTHOR = {Buhler, Joe and Crandall, Richard and Ernvall, Reijo and + Mets\"{a}nkyl\"{a}, Tauno and Shokrollahi, M. Amin}, + TITLE = {Irregular primes and cyclotomic invariants to 12 million}, + NOTE = {Computational algebra and number theory (Milwaukee, WI, 1996)}, + JOURNAL = {J. Symbolic Comput.}, + FJOURNAL = {Journal of Symbolic Computation}, + VOLUME = {31}, + YEAR = {2001}, + NUMBER = {1-2}, + PAGES = {89--96}, + ISSN = {0747-7171}, + MRCLASS = {11Y40 (11R18)}, + MRNUMBER = {1806208}, +MRREVIEWER = {Xavier-Fran\c{c}ois Roblot}, + DOI = {10.1006/jsco.1999.1011}, + URL = {https://doi.org/10.1006/jsco.1999.1011}, +} + +@article {MR778135, + AUTHOR = {Adleman, L. M. and Heath-Brown, D. R.}, + TITLE = {The first case of {F}ermat's last theorem}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {79}, + YEAR = {1985}, + NUMBER = {2}, + PAGES = {409--416}, + ISSN = {0020-9910}, + MRCLASS = {11D41}, + MRNUMBER = {778135}, +MRREVIEWER = {Takashi Agoh}, + DOI = {10.1007/BF01388981}, + URL = {https://doi.org/10.1007/BF01388981}, +} + +@article {MR491465, + AUTHOR = {Wagstaff, Jr., Samuel S.}, + TITLE = {The irregular primes to {$125000$}}, + JOURNAL = {Math. Comp.}, + FJOURNAL = {Mathematics of Computation}, + VOLUME = {32}, + YEAR = {1978}, + NUMBER = {142}, + PAGES = {583--591}, + ISSN = {0025-5718}, + MRCLASS = {10A40 (10B15 12A35)}, + MRNUMBER = {491465}, +MRREVIEWER = {Wells Johnson}, + DOI = {10.2307/2006167}, + URL = {https://doi.org/10.2307/2006167}, +} + +@article {MR3667037, + AUTHOR = {Hart, William and Harvey, David and Ong, Wilson}, + TITLE = {Irregular primes to two billion}, + JOURNAL = {Math. Comp.}, + FJOURNAL = {Mathematics of Computation}, + VOLUME = {86}, + YEAR = {2017}, + NUMBER = {308}, + PAGES = {3031--3049}, + ISSN = {0025-5718}, + MRCLASS = {11Y40 (11R18)}, + MRNUMBER = {3667037}, +MRREVIEWER = {Eleni Agathocli Agathocleous}, + DOI = {10.1090/mcom/3211}, + URL = {https://doi.org/10.1090/mcom/3211}, +} +@article {MR2813369, + AUTHOR = {Buhler, Joe and Harvey, David}, + TITLE = {Irregular primes to 163 million}, + JOURNAL = {Math. Comp.}, + FJOURNAL = {Mathematics of Computation}, + VOLUME = {80}, + YEAR = {2011}, + NUMBER = {276}, + PAGES = {2435--2444}, + ISSN = {0025-5718}, + MRCLASS = {11Y40 (11B68 11R18)}, + MRNUMBER = {2813369}, +MRREVIEWER = {Ali B. Ekin}, + DOI = {10.1090/S0025-5718-2011-02461-0}, + URL = {https://doi.org/10.1090/S0025-5718-2011-02461-0}, +} + +@book {MR1416327, + AUTHOR = {Edwards, Harold M.}, + TITLE = {Fermat's {L}ast {T}heorem}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {50}, + NOTE = {A genetic introduction to algebraic number theory, + Corrected reprint of the 1977 original}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1996}, + PAGES = {xvi+410}, + ISBN = {0-387-90230-9; 0-387-95002-8}, + MRCLASS = {11D41 (01A55 11-01)}, + MRNUMBER = {1416327}, +} + +@book {MR1029028, + AUTHOR = {Lang, Serge}, + TITLE = {Cyclotomic {F}ields {I} and {II}}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {121}, + EDITION = {second}, + NOTE = {With an appendix by Karl Rubin}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1990}, + PAGES = {xviii+433}, + ISBN = {0-387-96671-4}, + MRCLASS = {11-02 (11R18 11R20 11S40 11T22)}, + MRNUMBER = {1029028}, +MRREVIEWER = {T. Mets\"{a}nkyl\"{a}}, + DOI = {10.1007/978-1-4612-0987-4}, + URL = {https://doi.org/10.1007/978-1-4612-0987-4}, +} + +@book {MR1719329, + AUTHOR = {Ribenboim, Paulo}, + TITLE = {Fermat's {L}ast {T}heorem, for amateurs}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1999}, + PAGES = {xiv+407}, + ISBN = {0-387-98508-5}, + MRCLASS = {11D41 (00A08 01A05 11-01)}, + MRNUMBER = {1719329}, +MRREVIEWER = {Thomas John Tucker}, +} + +@book {MR1042981, + AUTHOR = {Fulton, William}, + TITLE = {Algebraic {C}urves}, + SERIES = {Advanced Book Classics}, + NOTE = {An introduction to algebraic geometry, + Notes written with the collaboration of Richard Weiss, + Reprint of 1969 original}, + PUBLISHER = {Addison-Wesley Publishing Company, Advanced Book Program, + Redwood City, CA}, + YEAR = {1989}, + PAGES = {xxii+226}, + ISBN = {0-201-51010-3}, + MRCLASS = {14Hxx (14-01)}, + MRNUMBER = {1042981}, +} + +@book {MR1955795, + AUTHOR = {Hulek, Klaus}, + TITLE = {Elementary {A}lgebraic {G}eometry}, + SERIES = {Student Mathematical Library}, + VOLUME = {20}, + NOTE = {Translated from the 2000 German original by Helena Verrill}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2003}, + PAGES = {viii+213}, + ISBN = {0-8218-2952-1}, + MRCLASS = {14-01}, + MRNUMBER = {1955795}, + DOI = {10.1090/stml/020}, + URL = {https://doi.org/10.1090/stml/020}, +} + + +@mastersthesis{Magiola, + author = {Μάριος Μαγιολαδίτης}, + title = { Αλγεβρικές καμπύλες, εικασία του Riemann και κωδικοποίηση}, + url ={https://www.researchgate.net/publication/32952663_Algebrikes_Kampyles_eikasia_tou_Riemann_kai_kodikopoiese}, + school = {Πανεπιστήμιο Κρήτης}, + year = {2001}, +} + + +@article {MR387283, + AUTHOR = {Serre, Jean-Pierre}, + TITLE = {Propri\'{e}t\'{e}s galoisiennes des points d'ordre fini des courbes + elliptiques}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {15}, + YEAR = {1972}, + NUMBER = {4}, + PAGES = {259--331}, + ISSN = {0020-9910}, + MRCLASS = {14G25 (14K15)}, + MRNUMBER = {387283}, +MRREVIEWER = {J. W. S. Cassels}, + DOI = {10.1007/BF01405086}, + URL = {https://doi.org/10.1007/BF01405086}, +} + +@incollection {MR902597, + AUTHOR = {Serre, J.-P.}, + TITLE = {Lettre \`a {J}.-{F}. {M}estre}, + BOOKTITLE = {Current trends in arithmetical algebraic geometry ({A}rcata, + {C}alif., 1985)}, + SERIES = {Contemp. Math.}, + VOLUME = {67}, + PAGES = {263--268}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {1987}, + MRCLASS = {11F80 (11F11)}, + MRNUMBER = {902597}, +MRREVIEWER = {Kenneth A. Ribet}, + DOI = {10.1090/conm/067/902597}, + URL = {https://doi.org/10.1090/conm/067/902597}, +} + +@article {MR885783, + AUTHOR = {Serre, Jean-Pierre}, + TITLE = {Sur les repr\'{e}sentations modulaires de degr\'{e} {$2$} de {${\rm + Gal}(\overline{\bf Q}/{\bf Q})$}}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {54}, + YEAR = {1987}, + NUMBER = {1}, + PAGES = {179--230}, + ISSN = {0012-7094}, + MRCLASS = {11F11 (11G05 14G15 14G25 14K15)}, + MRNUMBER = {885783}, +MRREVIEWER = {M. A. Kenku}, + DOI = {10.1215/S0012-7094-87-05413-5}, + URL = {https://doi.org/10.1215/S0012-7094-87-05413-5}, +} + +@article {MR2551763, + AUTHOR = {Khare, Chandrashekhar and Wintenberger, Jean-Pierre}, + TITLE = {Serre's modularity conjecture. {I}}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {178}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {485--504}, + ISSN = {0020-9910}, + MRCLASS = {11F80 (11F11 11F33 11R39)}, + MRNUMBER = {2551763}, +MRREVIEWER = {Gabor Wiese}, + DOI = {10.1007/s00222-009-0205-7}, + URL = {https://doi.org/10.1007/s00222-009-0205-7}, +} + +@article {MR2551764, + AUTHOR = {Khare, Chandrashekhar and Wintenberger, Jean-Pierre}, + TITLE = {Serre's modularity conjecture. {II}}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {178}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {505--586}, + ISSN = {0020-9910}, + MRCLASS = {11F80 (11F11 11F33 11R39)}, + MRNUMBER = {2551764}, +MRREVIEWER = {Gabor Wiese}, + DOI = {10.1007/s00222-009-0206-6}, + URL = {https://doi.org/10.1007/s00222-009-0206-6}, +} + +@article {MR2561373, + AUTHOR = {Frey, Gerhard}, + TITLE = {The {W}ay to the {P}roof of {F}ermat's {L}ast {T}heorem}, + JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)}, + FJOURNAL = {Annales de la Facult\'{e} des Sciences de Toulouse. Math\'{e}matiques. + S\'{e}rie 6}, + VOLUME = {18}, + YEAR = {2009}, + NUMBER = {Fascicule Sp\'{e}cial}, + PAGES = {5--23}, + ISSN = {0240-2963}, + MRCLASS = {11D41 (01A45 11G05)}, + MRNUMBER = {2561373}, +MRREVIEWER = {Robert Juricevic}, + URL = {http://afst.cedram.org/item?id=AFST_2009_6_18__5_0}, +} + +@book {MR2112196, + AUTHOR = {Diamond, Fred and Shurman, Jerry}, + TITLE = {A {F}irst {C}ourse in {M}odular {F}orms}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {228}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2005}, + PAGES = {xvi+436}, + ISBN = {0-387-23229-X}, + MRCLASS = {11Fxx}, + MRNUMBER = {2112196}, +MRREVIEWER = {Henri Darmon}, +} + +@book {MR574808, + AUTHOR = {Langlands, Robert P.}, + TITLE = {Base {C}hange for {${\rm GL}(2)$}}, + SERIES = {Annals of Mathematics Studies}, + VOLUME = {96}, + PUBLISHER = {Princeton University Press, Princeton, N.J.; University of + Tokyo Press, Tokyo}, + YEAR = {1980}, + PAGES = {vii+237}, + ISBN = {0-691-08263-4; 0-691-08272-3}, + MRCLASS = {10D40 (10-02 12A67 22E55)}, + MRNUMBER = {574808}, +MRREVIEWER = {Stephen Gelbart}, +} + +@article {MR621884, + AUTHOR = {Tunnell, Jerrold}, + TITLE = {Artin's conjecture for representations of octahedral type}, + JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, + FJOURNAL = {American Mathematical Society. Bulletin. New Series}, + VOLUME = {5}, + YEAR = {1981}, + NUMBER = {2}, + PAGES = {173--175}, + ISSN = {0273-0979}, + MRCLASS = {12A67 (10D40 10D45)}, + MRNUMBER = {621884}, +MRREVIEWER = {Stephen Gelbart}, + DOI = {10.1090/S0273-0979-1981-14936-3}, + URL = {https://doi.org/10.1090/S0273-0979-1981-14936-3}, +} + +@article {MR3617390, + AUTHOR = {Darmon, Henri}, + TITLE = {Andrew {W}iles's marvelous proof}, + JOURNAL = {Notices Amer. Math. Soc.}, + FJOURNAL = {Notices of the American Mathematical Society}, + VOLUME = {64}, + YEAR = {2017}, + NUMBER = {3}, + PAGES = {209--216}, + ISSN = {0002-9920}, + MRCLASS = {01A70}, + MRNUMBER = {3617390}, +} + +@article {MR1839918, + AUTHOR = {Breuil, Christophe and Conrad, Brian and Diamond, Fred and + Taylor, Richard}, + TITLE = {On the modularity of elliptic curves over {$\bold Q$}: wild + 3-adic exercises}, + JOURNAL = {J. Amer. Math. Soc.}, + FJOURNAL = {Journal of the American Mathematical Society}, + VOLUME = {14}, + YEAR = {2001}, + NUMBER = {4}, + PAGES = {843--939}, + ISSN = {0894-0347}, + MRCLASS = {11G05 (11F80 11G07 14G35)}, + MRNUMBER = {1839918}, +MRREVIEWER = {Karl Rubin}, + DOI = {10.1090/S0894-0347-01-00370-8}, + URL = {https://doi.org/10.1090/S0894-0347-01-00370-8}, +} + +@book {MR1989729, + AUTHOR = {Washington, Lawrence C.}, + TITLE = {Elliptic {C}urves}, + SERIES = {Discrete Mathematics and its Applications (Boca Raton)}, + NOTE = {Number theory and cryptography}, + PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL}, + YEAR = {2003}, + PAGES = {xii+428}, + ISBN = {1-58488-365-0}, + MRCLASS = {11G05 (11G20 14G50 94A60 94B27)}, + MRNUMBER = {1989729}, +MRREVIEWER = {Steven D. Galbraith}, +} + +@book {MR1860012, + TITLE = {Arithmetic {A}lgebraic {G}eometry}, + SERIES = {IAS/Park City Mathematics Series}, + VOLUME = {9}, + EDITOR = {Conrad, Brian and Rubin, Karl}, + NOTE = {Including papers from the Graduate Summer School of the + Institute for Advanced Study/Park City Mathematics Institute + held in Park City, UT, June 20--July 10, 1999}, + PUBLISHER = {American Mathematical Society, Providence, RI; Institute for + Advanced Study (IAS), Princeton, NJ}, + YEAR = {2001}, + PAGES = {xiv+569}, + ISBN = {0-8218-2173-3}, + MRCLASS = {11-06 (14-06)}, + MRNUMBER = {1860012}, +} + +@book {MR3243601, + AUTHOR = {Saito, Takeshi}, + TITLE = {Fermat's {L}ast {T}heorem}, + SERIES = {Translations of Mathematical Monographs}, + VOLUME = {245}, + NOTE = {The proof, + Translated from the 2009 Japanese original by Masato Kuwata, + Iwanami Series in Modern Mathematics}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2014}, + PAGES = {xvi+222}, + ISBN = {978-0-8218-9849-9}, + MRCLASS = {11D41 (11F11 11F80 11G05 11G18)}, + MRNUMBER = {3243601}, +MRREVIEWER = {B. Sury}, + DOI = {10.1090/mmono/245}, + URL = {https://doi.org/10.1090/mmono/245}, +} + +@book {MR3136492, + AUTHOR = {Saito, Takeshi}, + TITLE = {Fermat's last theorem}, + SERIES = {Translations of Mathematical Monographs}, + VOLUME = {243}, + NOTE = {Basic tools, + Translated from the Japanese original by Masato Kuwata}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2013}, + PAGES = {xiv+200}, + ISBN = {978-0-8218-9848-2}, + MRCLASS = {11D41 (11F11 11F80 11G05 11G18)}, + MRNUMBER = {3136492}, +MRREVIEWER = {Henri Darmon}, + DOI = {10.1090/mmono/243}, + URL = {https://doi.org/10.1090/mmono/243}, +} + +@article {MR1264001, + AUTHOR = {Gouv\^{e}a, Fernando Q.}, + TITLE = {``{A} marvelous proof''}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {101}, + YEAR = {1994}, + NUMBER = {3}, + PAGES = {203--222}, + ISSN = {0002-9890}, + MRCLASS = {11D41 (11G05 11G18)}, + MRNUMBER = {1264001}, +MRREVIEWER = {Henri Darmon}, + DOI = {10.2307/2975598}, + URL = {https://doi.org/10.2307/2975598}, +} + +@article {MR1256978, + AUTHOR = {Rubin, K. and Silverberg, A.}, + TITLE = {A report on {W}iles' {C}ambridge lectures}, + JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, + FJOURNAL = {American Mathematical Society. Bulletin. New Series}, + VOLUME = {31}, + YEAR = {1994}, + NUMBER = {1}, + PAGES = {15--38}, + ISSN = {0273-0979}, + MRCLASS = {11F80 (11D41 11G05)}, + MRNUMBER = {1256978}, +MRREVIEWER = {Richard Taylor}, + DOI = {10.1090/S0273-0979-1994-00512-9}, + URL = {https://doi.org/10.1090/S0273-0979-1994-00512-9}, +} + +@book {AntLocal, + AUTHOR = {Αντωνιάδης, Ιωάννης Α. }, + TITLE = {Σημειώσεις Τοπικών Σωμάτων}, + NOTE = {Πανεπιστήμιο Κρήτης, 1992}, + } + +@MASTERSTHESIS{KaraMaster, +AUTHOR={Καρανικολόπουλος Σωτήρης}, +TITLE={Uniformization Αλγεβρικών Καμπυλών}, +SCHOOL={Πανεπιστήμιο Αιγαίου, Μαθηματικό Τμήμα}, +YEAR={2005}, + } + + @article {Connes:Sel, + AUTHOR = {Connes, Alain}, + TITLE = {Trace formula in noncommutative geometry and the zeros of the + {R}iemann zeta function}, + JOURNAL = {Selecta Math. (N.S.)}, + FJOURNAL = {Selecta Mathematica. New Series}, + VOLUME = {5}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {29--106}, + ISSN = {1022-1824}, + CODEN = {SMATF6}, + MRCLASS = {11M26 (11R56 58B34)}, + MRNUMBER = {MR1694895 (2000i:11133)}, +MRREVIEWER = {Peter Sarnak}, +} + + +@book {MR1867354, + AUTHOR = {Hatcher, Allen}, + TITLE = {Algebraic topology}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2002}, + PAGES = {xii+544}, + ISBN = {0-521-79160-X; 0-521-79540-0}, + MRCLASS = {55-01 (55-00)}, + MRNUMBER = {1867354}, +MRREVIEWER = {Donald W. Kahn}, +} + +@incollection {MR902827, + AUTHOR = {Fouvry, \'{E}.}, + TITLE = {Sur le premier cas du th\'{e}or\`eme de {F}ermat}, + BOOKTITLE = {S\'{e}minaire de th\'{e}orie des nombres, {P}aris 1983--84}, + SERIES = {Progr. Math.}, + VOLUME = {59}, + PAGES = {91--104}, + PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, + YEAR = {1985}, + MRCLASS = {11D41 (11N13 11N35)}, + MRNUMBER = {902827}, +MRREVIEWER = {Takeo Miyoshi}, +} + +@book {MR1363488, + AUTHOR = {Lang, Serge}, + TITLE = {Introduction to modular forms}, + SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {222}, + NOTE = {With appendixes by D. Zagier and Walter Feit, + Corrected reprint of the 1976 original}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1995}, + PAGES = {x+261}, + ISBN = {3-540-07833-9}, + MRCLASS = {11Fxx}, + MRNUMBER = {1363488}, +} + + +@article {MR3764571, + AUTHOR = {Jones, Vaughan F. R.}, + TITLE = {A no-go theorem for the continuum limit of a periodic quantum + spin chain}, + JOURNAL = {Comm. Math. Phys.}, + FJOURNAL = {Communications in Mathematical Physics}, + VOLUME = {357}, + YEAR = {2018}, + NUMBER = {1}, + PAGES = {295--317}, + ISSN = {0010-3616}, + MRCLASS = {82B10 (81R12)}, + MRNUMBER = {3764571}, +MRREVIEWER = {Lawrence E. Thomas}, + DOI = {10.1007/s00220-017-2945-3}, + URL = {https://doi.org/10.1007/s00220-017-2945-3}, +} + + +@book {MR1878556, + AUTHOR = {Lang, Serge}, + TITLE = {Algebra}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {211}, + EDITION = {third}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2002}, + PAGES = {xvi+914}, + ISBN = {0-387-95385-X}, + MRCLASS = {00A05 (15-02)}, + MRNUMBER = {1878556}, + DOI = {10.1007/978-1-4613-0041-0}, + URL = {https://doi.org/10.1007/978-1-4613-0041-0}, +} + +@article {MR2534115, + AUTHOR = {Brewis, Louis Hugo and Wewers, Stefan}, + TITLE = {Artin characters, {H}urwitz trees and the lifting problem}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {345}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {711--730}, + ISSN = {0025-5831}, + MRCLASS = {14G20 (11S31 13F25 14H30 14H37 14L30)}, + MRNUMBER = {2534115}, +MRREVIEWER = {Daniel Barsky}, + DOI = {10.1007/s00208-009-0374-0}, + URL = {https://doi.org/10.1007/s00208-009-0374-0}, +} + +@article {MR3069638, + AUTHOR = {Chevalley, C. and Weil, A. and Hecke, E.}, + TITLE = {\"{U}ber das verhalten der integrale 1. gattung bei automorphismen + des funktionenk\"{o}rpers}, + JOURNAL = {Abh. Math. Sem. Univ. Hamburg}, + FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t + Hamburg}, + VOLUME = {10}, + YEAR = {1934}, + NUMBER = {1}, + PAGES = {358--361}, + ISSN = {0025-5858}, + MRCLASS = {DML}, + MRNUMBER = {3069638}, + DOI = {10.1007/BF02940687}, + URL = {https://doi.org/10.1007/BF02940687}, +} + + + + + + +@book {MR506881, + AUTHOR = {Hazewinkel, Michiel}, + TITLE = {Formal groups and applications}, + SERIES = {Pure and Applied Mathematics}, + VOLUME = {78}, + PUBLISHER = {Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], + New York-London}, + YEAR = {1978}, + PAGES = {xxii+573pp}, + ISBN = {0-12-335150-2}, + MRCLASS = {14L05 (10D30 12B25 55N22)}, + MRNUMBER = {506881}, +MRREVIEWER = {Robert A. Morris}, +} + +@article {MR3556796, + AUTHOR = {Obus, Andrew}, + TITLE = {The local lifting problem for {$A_4$}}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {10}, + YEAR = {2016}, + NUMBER = {8}, + PAGES = {1683--1693}, + ISSN = {1937-0652}, + MRCLASS = {14H37 (12F10 13B05 14B12)}, + MRNUMBER = {3556796}, +MRREVIEWER = {Marko Roczen}, + DOI = {10.2140/ant.2016.10.1683}, + URL = {https://doi.org/10.2140/ant.2016.10.1683}, +} + + +@article {MR2525558, + AUTHOR = {Himstedt, Frank and Symonds, Peter}, + TITLE = {Equivariant {H}ilbert series}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {3}, + YEAR = {2009}, + NUMBER = {4}, + PAGES = {423--443}, + ISSN = {1937-0652}, + MRCLASS = {13D40 (20C20)}, + MRNUMBER = {2525558}, +MRREVIEWER = {Adam L. Van Tuyl}, + DOI = {10.2140/ant.2009.3.423}, + URL = {https://doi.org/10.2140/ant.2009.3.423}, +} + +@article {MR1274097, + AUTHOR = {Chinburg, Ted}, + TITLE = {Galois structure of de {R}ham cohomology of tame covers of + schemes}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {139}, + YEAR = {1994}, + NUMBER = {2}, + PAGES = {443--490}, + ISSN = {0003-486X}, + MRCLASS = {11R33 (14F40 14G10)}, + MRNUMBER = {1274097}, +MRREVIEWER = {Boas Erez}, + DOI = {10.2307/2946586}, + URL = {https://doi.org/10.2307/2946586}, +} + +@article{Chinburg1996TameAO, + title={Tame actions of group schemes: integrals and slices}, + author={T. Chinburg and B. Erez and G. Pappas and M. Taylor}, + journal={Duke Mathematical Journal}, + year={1996}, + volume={82}, + pages={269-308} +} + +@article {MR3874854, + AUTHOR = {Weaver, Bradley}, + TITLE = {The local lifting problem for {$D_4$}}, + JOURNAL = {Israel J. Math.}, + FJOURNAL = {Israel Journal of Mathematics}, + VOLUME = {228}, + YEAR = {2018}, + NUMBER = {2}, + PAGES = {587--626}, + ISSN = {0021-2172}, + MRCLASS = {14H37 (12F10)}, + MRNUMBER = {3874854}, +MRREVIEWER = {Valentijn Zo\"{e} Karemaker}, + DOI = {10.1007/s11856-018-1782-1}, + URL = {https://doi.org/10.1007/s11856-018-1782-1}, +} + +@book {MR2868112, + AUTHOR = {Stanley, Richard P.}, + TITLE = {Enumerative combinatorics. {V}olume 1}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {49}, + EDITION = {Second}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2012}, + PAGES = {xiv+626}, + ISBN = {978-1-107-60262-5}, + MRCLASS = {05-02 (05A15 06-02)}, + MRNUMBER = {2868112}, +} + +@book {MR1251956, + AUTHOR = {Bruns, Winfried and Herzog, J\"{u}rgen}, + TITLE = {Cohen-{M}acaulay rings}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {39}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1993}, + PAGES = {xii+403}, + ISBN = {0-521-41068-1}, + MRCLASS = {13H10 (13-02)}, + MRNUMBER = {1251956}, +MRREVIEWER = {Matthew Miller}, +} + +@inproceedings{MR4144024, + AUTHOR = {Charalambous, Hara and Karagiannis, Kostas and + Karanikolopoulos, Sotiris and Kontogeorgis, Aristides}, + TITLE = {Syzygies of ideals of polynomial rings over principal ideal + domains}, + BOOKTITLE = {I{SSAC}'20---{P}roceedings of the 45th {I}nternational + {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}, + PAGES = {78--82}, + PUBLISHER = {ACM, New York}, + YEAR = {[2020] \copyright 2020}, + MRCLASS = {13D02 (68W30)}, + MRNUMBER = {4144024}, + DOI = {10.1145/3373207.3404046}, + URL = {https://doi.org/10.1145/3373207.3404046}, +} + + +url = {https://doi.org/10.1145/3373207.3404046}, +doi = {10.1145/3373207.3404046}, +abstract = {We study computational aspects of syzygies of graded modules over polynomial rings R[w1, ..., wg] when the base R is a discrete valuation ring. In particular, we use the torsion of their syzygies over R to provide a formula which describes the behavior of the Betti numbers when changing the base to the residue field or the fraction field of R. Our work is motivated by the deformation theory of curves.}, +booktitle = {Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation}, +pages = {78–82}, +numpages = {5}, +keywords = {lifting MSC:13D02, 13P20, principal ideal domains, syzygies, commutive algebra, reduction}, +location = {Kalamata, Greece}, +series = {ISSAC '20} +} + +@article {MR526968, + AUTHOR = {Stanley, Richard P.}, + TITLE = {Invariants of finite groups and their applications to + combinatorics}, + JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, + FJOURNAL = {American Mathematical Society. Bulletin. New Series}, + VOLUME = {1}, + YEAR = {1979}, + NUMBER = {3}, + PAGES = {475--511}, + ISSN = {0273-0979}, + MRCLASS = {20C15 (05A15 13H10 14H10 15A72 51F15)}, + MRNUMBER = {526968}, +MRREVIEWER = {Ralph Strebel}, + DOI = {10.1090/S0273-0979-1979-14597-X}, + URL = {https://doi.org/10.1090/S0273-0979-1979-14597-X}, +} + +@article {MR2304322, + AUTHOR = {Symonds, Peter}, + TITLE = {Structure theorems over polynomial rings}, + JOURNAL = {Adv. Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {208}, + YEAR = {2007}, + NUMBER = {1}, + PAGES = {408--421}, + ISSN = {0001-8708}, + MRCLASS = {20C05}, + MRNUMBER = {2304322}, +MRREVIEWER = {Mark L. Lewis}, + DOI = {10.1016/j.aim.2006.02.012}, + URL = {https://doi.org/10.1016/j.aim.2006.02.012}, +} + +@article {MR608528, + AUTHOR = {Taylor, M. J.}, + TITLE = {On {F}r\"{o}hlich's conjecture for rings of integers of tame + extensions}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {63}, + YEAR = {1981}, + NUMBER = {1}, + PAGES = {41--79}, + ISSN = {0020-9910}, + MRCLASS = {12A55 (12A57)}, + MRNUMBER = {608528}, +MRREVIEWER = {Hans Opolka}, + DOI = {10.1007/BF01389193}, + URL = {https://doi.org/10.1007/BF01389193}, +} + +@article {MR589254, + AUTHOR = {Ellingsrud, G. and L{\o}nsted, K.}, + TITLE = {An equivariant {L}efschetz formula for finite reductive + groups}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {251}, + YEAR = {1980}, + NUMBER = {3}, + PAGES = {253--261}, + ISSN = {0025-5831}, + MRCLASS = {14L30 (55M99)}, + MRNUMBER = {589254}, +MRREVIEWER = {H. H. Andersen}, + DOI = {10.1007/BF01428945}, + URL = {https://doi.org/10.1007/BF01428945}, +} + +@article {MR1753111, + AUTHOR = {Pappas, Georgios}, + TITLE = {Galois module structure and the {$\gamma$}-filtration}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {121}, + YEAR = {2000}, + NUMBER = {1}, + PAGES = {79--104}, + ISSN = {0010-437X}, + MRCLASS = {14F05 (11R33 14C35 19A31 19E08)}, + MRNUMBER = {1753111}, +MRREVIEWER = {Nigel Byott}, + DOI = {10.1023/A:1001722414377}, + URL = {https://doi.org/10.1023/A:1001722414377}, +} + +@book {MR2590895, + AUTHOR = {Brou\'{e}, Michel}, + TITLE = {Introduction to complex reflection groups and their braid + groups}, + SERIES = {Lecture Notes in Mathematics}, + VOLUME = {1988}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2010}, + PAGES = {xii+138}, + ISBN = {978-3-642-11174-7}, + MRCLASS = {20F55 (20F36 57M07)}, + MRNUMBER = {2590895}, +MRREVIEWER = {Stephen P. Humphries}, + DOI = {10.1007/978-3-642-11175-4}, + URL = {https://doi.org/10.1007/978-3-642-11175-4}, +} + +@incollection {MR2027446, + AUTHOR = {Tevelev, E. A.}, + TITLE = {Projectively dual varieties}, + NOTE = {Algebraic geometry}, + JOURNAL = {J. Math. Sci. (N.Y.)}, + FJOURNAL = {Journal of Mathematical Sciences (New York)}, + VOLUME = {117}, + YEAR = {2003}, + NUMBER = {6}, + PAGES = {4585--4732}, + ISSN = {1072-3374}, + MRCLASS = {14N05 (14J17 14L30 14N15)}, + MRNUMBER = {2027446}, +MRREVIEWER = {Dan Avritzer}, + DOI = {10.1023/A:1025366207448}, + URL = {https://doi.org/10.1023/A:1025366207448}, +} + +@book {MR834791, + AUTHOR = {Hasse, Helmut}, + TITLE = {\"{U}ber die {K}lassenzahl abelscher {Z}ahlk\"{o}rper}, + NOTE = {Reprint of the 1952 edition, + With an introduction to the reprint edition by Jacques + Martinet}, + PUBLISHER = {Akademie-Verlag, Berlin}, + YEAR = {1985}, + PAGES = {12+xii+190}, + MRCLASS = {11R29 (01A75)}, + MRNUMBER = {834791}, + DOI = {10.1007/978-3-642-69886-6}, + URL = {https://doi.org/10.1007/978-3-642-69886-6}, +} + + +@article {MR0021031, + AUTHOR = {Kuroda, Sigekatu}, + TITLE = {\"{U}ber den {D}irichletschen {K}\"{o}rper}, + JOURNAL = {J. Fac. Sci. Imp. Univ. Tokyo Sect. I.}, + VOLUME = {4}, + YEAR = {1943}, + PAGES = {383--406}, + MRCLASS = {10.0X}, + MRNUMBER = {0021031}, +MRREVIEWER = {M. Krasner}, +} + +@article {MR83009, + AUTHOR = {Kubota, Tomio}, + TITLE = {\"{U}ber den bizyklischen biquadratischen {Z}ahlk\"{o}rper}, + JOURNAL = {Nagoya Math. J.}, + FJOURNAL = {Nagoya Mathematical Journal}, + VOLUME = {10}, + YEAR = {1956}, + PAGES = {65--85}, + ISSN = {0027-7630}, + MRCLASS = {10.2X}, + MRNUMBER = {83009}, +MRREVIEWER = {G. Whaples}, + URL = {http://projecteuclid.org/euclid.nmj/1118799770}, +} + +@article {MR1576157, + AUTHOR = {Berwick, W. E. H.}, + TITLE = {Algebraic {N}umber-{F}ields with two {I}ndependent {U}nits}, + JOURNAL = {Proc. London Math. Soc. (2)}, + FJOURNAL = {Proceedings of the London Mathematical Society. Second Series}, + VOLUME = {34}, + YEAR = {1932}, + NUMBER = {5}, + PAGES = {360--378}, + ISSN = {0024-6115}, + MRCLASS = {DML}, + MRNUMBER = {1576157}, + DOI = {10.1112/plms/s2-34.1.360}, + URL = {https://doi.org/10.1112/plms/s2-34.1.360}, +} + +@book {MR584794, + AUTHOR = {M\"{a}ki, Sirpa}, + TITLE = {The determination of units in real cyclic sextic fields}, + SERIES = {Lecture Notes in Mathematics}, + VOLUME = {797}, + PUBLISHER = {Springer, Berlin}, + YEAR = {1980}, + PAGES = {i+198}, + ISBN = {3-540-09984-0}, + MRCLASS = {12A45 (12A35 12A50)}, + MRNUMBER = {584794}, +MRREVIEWER = {Charles J. Parry}, +} + +@article {MR1031243, + AUTHOR = {Shen, Yuan Yuan}, + TITLE = {Unit groups and class numbers of real cyclic octic fields}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {326}, + YEAR = {1991}, + NUMBER = {1}, + PAGES = {179--209}, + ISSN = {0002-9947}, + MRCLASS = {11R20 (11R27 11R29)}, + MRNUMBER = {1031243}, +MRREVIEWER = {H. Yokoi}, + DOI = {10.2307/2001860}, + URL = {https://doi.org/10.2307/2001860}, +} + + +@book {MR3495343, + AUTHOR = {Olsson, Martin}, + TITLE = {Algebraic spaces and stacks}, + SERIES = {American Mathematical Society Colloquium Publications}, + VOLUME = {62}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2016}, + PAGES = {xi+298}, + ISBN = {978-1-4704-2798-6}, + MRCLASS = {14D23 (14D22)}, + MRNUMBER = {3495343}, +MRREVIEWER = {Stefan Schr\"{o}er}, + DOI = {10.1090/coll/062}, + URL = {https://doi.org/10.1090/coll/062}, +} + + +@misc{210600004, +Author = {Lhoussain El Fadil}, +Title = {A note ON MONOGENEITY of pure number fields}, +Year = {2021}, +url = {arXiv:2106.00004}, +} + +@misc{ΝΝ, +Author = {N. Nitsure}, +Title = {Notes on Deformation Theory, Guanajuato}, +Year = {2006}, +URL ={https://cel.archives-ouvertes.fr/cel-00392119}, +} + +@MastersThesis{Terez, + author = {Αλέξιος Τερεζάκης}, + title = {Deformation Theory}, + school = {Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών}, + year = {2019}, + +} + +@article {KodSpenc, + AUTHOR = {Kodaira, K. and Spencer, D. C.}, + TITLE = {On deformations of complex analytic structures. {I}, {II}}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {67}, + YEAR = {1958}, + PAGES = {328--466}, + ISSN = {0003-486X}, + MRCLASS = {57.00}, + MRNUMBER = {112154}, +MRREVIEWER = {M. F. Atiyah}, + DOI = {10.2307/1970009}, + URL = {https://doi.org/10.2307/1970009}, +} + +@book {MR1326604, + AUTHOR = {Miranda, Rick}, + TITLE = {Algebraic curves and {R}iemann surfaces}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {5}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {1995}, + PAGES = {xxii+390}, + ISBN = {0-8218-0268-2}, + MRCLASS = {14Hxx (14-01 30F99)}, + MRNUMBER = {1326604}, +MRREVIEWER = {R. F. Lax}, + DOI = {10.1090/gsm/005}, + URL = {https://doi.org/10.1090/gsm/005}, +} + +@book {mig, +AUTHOR = {Churchill, R. and Brown, J.}, + TITLE = {Μιγαδικές Συναρτήσεις και εφαρμογές 2η έκδοση}, + PUBLISHER ={Πανεπιστημιακές Εκδόσεις Κρήτης}, + YEAR = {1998}, +} + +@book {MR648106, + AUTHOR = {Forster, Otto}, + TITLE = {Lectures on {R}iemann surfaces}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {81}, + NOTE = {Translated from the German by Bruce Gilligan}, + PUBLISHER = {Springer-Verlag, New York-Berlin}, + YEAR = {1981}, + PAGES = {viii+254}, + ISBN = {0-387-90617-7}, + MRCLASS = {30Fxx (14-01 32-01)}, + MRNUMBER = {648106}, +} + +@book {MR1138207, + AUTHOR = {do Carmo, Manfredo Perdig\~{a}o}, + TITLE = {Riemannian geometry}, + SERIES = {Mathematics: Theory \& Applications}, + NOTE = {Translated from the second Portuguese edition by Francis + Flaherty}, + PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA}, + YEAR = {1992}, + PAGES = {xiv+300}, + ISBN = {0-8176-3490-8}, + MRCLASS = {53-01}, + MRNUMBER = {1138207}, +MRREVIEWER = {Bang-yen Chen}, + DOI = {10.1007/978-1-4757-2201-7}, + URL = {https://doi.org/10.1007/978-1-4757-2201-7}, +} + +@book {MR510197, + AUTHOR = {Ahlfors, Lars V.}, + TITLE = {Complex analysis}, + SERIES = {International Series in Pure and Applied Mathematics}, + EDITION = {Third}, + NOTE = {An introduction to the theory of analytic functions of one + complex variable}, + PUBLISHER = {McGraw-Hill Book Co., New York}, + YEAR = {1978}, + PAGES = {xi+331}, + ISBN = {0-07-000657-1}, + MRCLASS = {30-01}, + MRNUMBER = {510197}, +} + +@book {MR1336822, + AUTHOR = {Hirsch, Morris W.}, + TITLE = {Differential topology}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {33}, + NOTE = {Corrected reprint of the 1976 original}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1994}, + PAGES = {x+222}, + ISBN = {0-387-90148-5}, + MRCLASS = {57-01 (58-01)}, + MRNUMBER = {1336822}, +} + + + +@article {GAGA, + AUTHOR = {Serre, Jean-Pierre}, + TITLE = {G\'{e}om\'{e}trie alg\'{e}brique et g\'{e}om\'{e}trie analytique}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {6}, + YEAR = {1955/56}, + PAGES = {1--42}, + ISSN = {0373-0956}, + MRCLASS = {53.3X}, + MRNUMBER = {82175}, +MRREVIEWER = {H. Cartan}, + URL = {http://aif.cedram.org/item?id=AIF_1955__6__1_0}, +} + +@book {MR1748380, + AUTHOR = {Mumford, David}, + TITLE = {The red book of varieties and schemes}, + SERIES = {Lecture Notes in Mathematics}, + VOLUME = {1358}, + EDITION = {expanded}, + NOTE = {Includes the Michigan lectures (1974) on curves and their + Jacobians, + With contributions by Enrico Arbarello}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1999}, + PAGES = {x+306}, + ISBN = {3-540-63293-X}, + MRCLASS = {14-01 (14A15 14H40 14H42)}, + MRNUMBER = {1748380}, +MRREVIEWER = {Arnaud Beauville}, + DOI = {10.1007/b62130}, + URL = {https://doi.org/10.1007/b62130}, +} + + +@book {GathmannAG, +AUTHOR = {Gathmann, A.}, + TITLE = {Algebraic Geometry}, + PUBLISHER ={Lecture Notes}, + YEAR = {2020}, + url = {https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2019/alggeom-2019.pdf}, +} + +@book {MR1166800, + AUTHOR = {Eisenbud, David and Harris, Joe}, + TITLE = {Schemes}, + SERIES = {The Wadsworth \& Brooks/Cole Mathematics Series}, + NOTE = {The language of modern algebraic geometry}, + PUBLISHER = {Wadsworth \& Brooks/Cole Advanced Books \& Software, Pacific + Grove, CA}, + YEAR = {1992}, + PAGES = {xii+157}, + ISBN = {0-534-17606-2; 0-534-17604-6}, + MRCLASS = {14-01 (14A15)}, + MRNUMBER = {1166800}, +MRREVIEWER = {Alexey N. Rudakov}, +} + + +@book {MatzatWP, +AUTHOR = {Matzat, H. }, + TITLE = {Ein {V}ortrag \"uber {W}eierstrasspunkte}, + PUBLISHER ={Karlsruhe}, + YEAR = {1975}, +} + +@article{1905.05545, +Author = {Hara Charalambous and Kostas Karagiannis and Aristides Kontogeorgis}, +Title = {The Relative Canonical Ideal of the {A}rtin-{S}chreier-{K}ummer-{W}itt family of curves}, +Year = {2023}, + +journal = {Annales de l'institut Fourier}, +url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3543/ +}, +DOI ={10.5802/aif.3543}, +volume = {73}, +PAGES = {1085-1113}, +NUMBER ={3}, +} + +@incollection {MR3986040, + AUTHOR = {Jones, Vaughan F. R.}, + TITLE = {On the construction of knots and links from {T}hompson's + groups}, + BOOKTITLE = {Knots, low-dimensional topology and applications}, + SERIES = {Springer Proc. Math. Stat.}, + VOLUME = {284}, + PAGES = {43--66}, + PUBLISHER = {Springer, Cham}, + YEAR = {2019}, + MRCLASS = {57M25 (20F36 20F38 22D10 57M27)}, + MRNUMBER = {3986040}, + DOI = {10.1007/978-3-030-16031-9\_3}, + URL = {https://doi.org/10.1007/978-3-030-16031-9_3}, +} + +@article {MR3589908, + AUTHOR = {Jones, Vaughan F. R.}, + TITLE = {Some unitary representations of {T}hompson's groups {$F$} and + {$T$}}, + JOURNAL = {J. Comb. Algebra}, + FJOURNAL = {Journal of Combinatorial Algebra}, + VOLUME = {1}, + YEAR = {2017}, + NUMBER = {1}, + PAGES = {1--44}, + ISSN = {2415-6302}, + MRCLASS = {57M25 (20F38 46L37 81T40)}, + MRNUMBER = {3589908}, +MRREVIEWER = {Conchita Mart\'{\i}nez-P\'{e}rez}, + DOI = {10.4171/JCA/1-1-1}, + URL = {https://doi.org/10.4171/JCA/1-1-1}, +} + +@article {MR3003928, + AUTHOR = {Juyumaya, Jes\'{u}s and Lambropoulou, Sofia}, + TITLE = {{$p$}-adic framed braids {II}}, + NOTE = {With an appendix by Paul G\'{e}rardin}, + JOURNAL = {Adv. Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {234}, + YEAR = {2013}, + PAGES = {149--191}, + ISSN = {0001-8708}, + MRCLASS = {20F36 (20C08 57M27)}, + MRNUMBER = {3003928}, + DOI = {10.1016/j.aim.2012.10.011}, + URL = {https://doi.org/10.1016/j.aim.2012.10.011}, +} + +@article {MR2317081, + AUTHOR = {Juyumaya, J. and Lambropoulou, S.}, + TITLE = {{$p$}-adic framed braids}, + JOURNAL = {Topology Appl.}, + FJOURNAL = {Topology and its Applications}, + VOLUME = {154}, + YEAR = {2007}, + NUMBER = {8}, + PAGES = {1804--1826}, + ISSN = {0166-8641}, + MRCLASS = {57M27}, + MRNUMBER = {2317081}, +MRREVIEWER = {James Roger Conant}, + DOI = {10.1016/j.topol.2007.01.010}, + URL = {https://doi.org/10.1016/j.topol.2007.01.010}, +} + + +@MISC {244876, + TITLE = {Uniqueness of sums of roots of unity}, + AUTHOR = {itotcg (https://mathoverflow.net/users/95358/itotcg)}, + HOWPUBLISHED = {MathOverflow}, + NOTE = {URL:https://mathoverflow.net/q/244876 (version: 2017-04-13)}, + EPRINT = {https://mathoverflow.net/q/244876}, + URL = {https://mathoverflow.net/q/244876} +} + +@article {MR1736695, + AUTHOR = {Lam, T. Y. and Leung, K. H.}, + TITLE = {On vanishing sums of roots of unity}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {224}, + YEAR = {2000}, + NUMBER = {1}, + PAGES = {91--109}, + ISSN = {0021-8693}, + MRCLASS = {11L03}, + MRNUMBER = {1736695}, +MRREVIEWER = {Martin W. Liebeck}, + DOI = {10.1006/jabr.1999.8089}, + URL = {https://doi.org/10.1006/jabr.1999.8089}, +} + +@article {MR191892, + AUTHOR = {Mann, Henry B.}, + TITLE = {On linear relations between roots of unity}, + JOURNAL = {Mathematika}, + FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics}, + VOLUME = {12}, + YEAR = {1965}, + PAGES = {107--117}, + ISSN = {0025-5793}, + MRCLASS = {52.10 (10.66)}, + MRNUMBER = {191892}, +MRREVIEWER = {H. Schwerdtfeger}, + DOI = {10.1112/S0025579300005210}, + URL = {https://doi.org/10.1112/S0025579300005210}, +} + +@article {MR1426438, + AUTHOR = {Cannon, J. W. and Floyd, W. J. and Parry, W. R.}, + TITLE = {Introductory notes on {R}ichard {T}hompson's groups}, + JOURNAL = {Enseign. Math. (2)}, + FJOURNAL = {L'Enseignement Math\'{e}matique. Revue Internationale. 2e S\'{e}rie}, + VOLUME = {42}, + YEAR = {1996}, + NUMBER = {3-4}, + PAGES = {215--256}, + ISSN = {0013-8584}, + MRCLASS = {20F32 (57M07)}, + MRNUMBER = {1426438}, +MRREVIEWER = {Michael L. Mihalik}, +URL = {https://doi.org/10.4171/JCA/1-1-1}, +} + +@article{charalambous2021equivariant, + title={The equivariant Hilbert series of the canonical ring of Fermat curves}, + author={Hara Charalambous and Kostas Karagiannis and Sotiris Karanikolopoulos and Aristides Kontogeorgis}, + year={2022}, + eprint={2105.06945}, + archivePrefix={arXiv}, + JOURNAL={Indagationes Mathematicae (accepted)}, + FJOURNAL={Indagationes Mathematicae (accepted)}, + doi = {https://doi.org/10.1016/j.indag.2022.06.001}, + primaryClass={math.AG} +} + +@misc{charalambous2022Conf, + title={Computational Aspects of Equivariant Hilbert Series of Canonical Rings for Algebraic Curves }, + author={Hara Charalambous and Kostas Karagiannis and Sotiris Karanikolopoulos and Aristides Kontogeorgis}, + year={2022}, + eprint={Lecture Notes in Computer Science}, + primaryClass={math.AG} +} + + +@article {MR151948, + AUTHOR = {Lickorish, W. B. R.}, + TITLE = {A representation of orientable combinatorial {$3$}-manifolds}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {76}, + YEAR = {1962}, + PAGES = {531--540}, + ISSN = {0003-486X}, + MRCLASS = {54.78}, + MRNUMBER = {151948}, +MRREVIEWER = {A. D. Wallace}, + DOI = {10.2307/1970373}, + URL = {https://doi.org/10.2307/1970373}, +} + +@article {MR125588, + AUTHOR = {Wallace, Andrew H.}, + TITLE = {Modifications and cobounding manifolds}, + JOURNAL = {Canadian J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {12}, + YEAR = {1960}, + PAGES = {503--528}, + ISSN = {0008-414X}, + MRCLASS = {57.10}, + MRNUMBER = {125588}, +MRREVIEWER = {Morris W. Hirsch}, + DOI = {10.4153/CJM-1960-045-7}, + URL = {https://doi.org/10.4153/CJM-1960-045-7}, +} + +@article {MR4071378, + AUTHOR = {Aiello, Valeriano}, + TITLE = {On the {A}lexander theorem for the oriented {T}hompson group + {$\overrightarrow{F}$}}, + JOURNAL = {Algebr. Geom. Topol.}, + FJOURNAL = {Algebraic \& Geometric Topology}, + VOLUME = {20}, + YEAR = {2020}, + NUMBER = {1}, + PAGES = {429--438}, + ISSN = {1472-2747}, + MRCLASS = {57K10}, + MRNUMBER = {4071378}, +MRREVIEWER = {Masakazu Teragaito}, + DOI = {10.2140/agt.2020.20.429}, + URL = {https://doi.org/10.2140/agt.2020.20.429}, +} + +@misc{2008.11052, +Author = {Rushil Raghavan and Dennis Sweeney}, +Title = {Regular Isotopy Classes of Link Diagrams From Thompson's Groups}, +Year = {2020}, +Eprint = {arXiv:2008.11052}, +} + +@article {MR2328711, + AUTHOR = {Karagueuzian, Dikran B. and Symonds, Peter}, + TITLE = {The module structure of a group action on a polynomial ring: a + finiteness theorem}, + JOURNAL = {J. Amer. Math. Soc.}, + FJOURNAL = {Journal of the American Mathematical Society}, + VOLUME = {20}, + YEAR = {2007}, + NUMBER = {4}, + PAGES = {931--967}, + ISSN = {0894-0347}, + MRCLASS = {20C20 (13A50)}, + MRNUMBER = {2328711}, +MRREVIEWER = {U\u{g}ur Madran}, + DOI = {10.1090/S0894-0347-07-00563-2}, + URL = {https://doi.org/10.1090/S0894-0347-07-00563-2}, +} + +@incollection {MR2066462, + AUTHOR = {Karagueuzian, D. B. and Symonds, P.}, + TITLE = {The module structure of a group action on a polynomial ring: + examples, generalizations, and applications}, + BOOKTITLE = {Invariant theory in all characteristics}, + SERIES = {CRM Proc. Lecture Notes}, + VOLUME = {35}, + PAGES = {139--158}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {2004}, + MRCLASS = {13A50 (20C20)}, + MRNUMBER = {2066462}, +MRREVIEWER = {Thomas Bayer}, + DOI = {10.1090/crmp/035/08}, + URL = {https://doi.org/10.1090/crmp/035/08}, +} + +@article {MR2328711, + AUTHOR = {Karagueuzian, Dikran B. and Symonds, Peter}, + TITLE = {The module structure of a group action on a polynomial ring: a + finiteness theorem}, + JOURNAL = {J. Amer. Math. Soc.}, + FJOURNAL = {Journal of the American Mathematical Society}, + VOLUME = {20}, + YEAR = {2007}, + NUMBER = {4}, + PAGES = {931--967}, + ISSN = {0894-0347}, + MRCLASS = {20C20 (13A50)}, + MRNUMBER = {2328711}, +MRREVIEWER = {U\u{g}ur Madran}, + DOI = {10.1090/S0894-0347-07-00563-2}, + URL = {https://doi.org/10.1090/S0894-0347-07-00563-2}, +} + + +@book {MR0171899, + AUTHOR = {Markushevich, A. I.}, + TITLE = {Theory of functions of a complex variable. {V}ol. {I}}, + NOTE = {Translated and edited by Richard A. Silverman}, + PUBLISHER = {Prentice-Hall, Inc., Englewood Cliffs, N.J.}, + YEAR = {1965}, + PAGES = {xiv+459}, + MRCLASS = {30.00}, + MRNUMBER = {0171899}, +MRREVIEWER = {R. P. Boas, Jr.}, +} + + +@phdthesis{TimDokchitserPhd, + author = {Dokchitser, Tim}, + title = {Deformations of $p$-divisible groups and $p$-descent on elliptic curves}, + school = {Universiteit Utrecht}, + year = {2000}, + +} + +@MISC {292813, + TITLE = {Relation between the Hochschild cohomology of group algebras and groupoids}, + AUTHOR = {Yonatan Harpaz (https://mathoverflow.net/users/51164/yonatan-harpaz)}, + HOWPUBLISHED = {MathOverflow}, + NOTE = {URL:https://mathoverflow.net/q/292813 (version: 2018-02-14)}, + EPRINT = {https://mathoverflow.net/q/292813}, + URL = {https://mathoverflow.net/q/292813} +} + +@article {MR2959787, + AUTHOR = {Dekimpe, Karel and Hartl, Manfred and Wauters, Sarah}, + TITLE = {A seven-term exact sequence for the cohomology of a group + extension}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {369}, + YEAR = {2012}, + PAGES = {70--95}, + ISSN = {0021-8693}, + MRCLASS = {20J06}, + MRNUMBER = {2959787}, +MRREVIEWER = {Gerald Williams}, + DOI = {10.1016/j.jalgebra.2012.07.009}, + URL = {https://doi.org/10.1016/j.jalgebra.2012.07.009}, +} + + +@misc{2101.11084, +Author = {Aristides Kontogeorgis and Alexios Terezakis}, +Title = {The canonical ideal and the deformation theory of curves with automorphisms}, +Year = {2021}, +Eprint = {arXiv:2101.11084}, +} + + + + +@article {MR3556796, + AUTHOR = {Obus, Andrew}, + TITLE = {The local lifting problem for {$A_4$}}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {10}, + YEAR = {2016}, + NUMBER = {8}, + PAGES = {1683--1693}, + ISSN = {1937-0652}, + MRCLASS = {14H37 (12F10 13B05 14B12)}, + MRNUMBER = {3556796}, +MRREVIEWER = {Marko Roczen}, + DOI = {10.2140/ant.2016.10.1683}, + URL = {https://doi.org/10.2140/ant.2016.10.1683}, +} + +@article {MR2254623, + AUTHOR = {Bouw, Irene I. and Wewers, Stefan}, + TITLE = {The local lifting problem for dihedral groups}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {134}, + YEAR = {2006}, + NUMBER = {3}, + PAGES = {421--452}, + ISSN = {0012-7094}, + MRCLASS = {14H37 (11G20 14D15)}, + MRNUMBER = {2254623}, +MRREVIEWER = {Marko Roczen}, + DOI = {10.1215/S0012-7094-06-13431-2}, + URL = {https://doi.org/10.1215/S0012-7094-06-13431-2}, +} + +@phdthesis{PagotPhd, + author = {Pagot, Guillaume}, + title = {Relèvement en caractéristique zéro d'actions de groupes abéliens de type $(p,\ldots,p)$}, + school = {Bordeaux Univeristy}, + year = {2002}, +} + +@article {MR3874854, + AUTHOR = {Weaver, Bradley}, + TITLE = {The local lifting problem for {$D_4$}}, + JOURNAL = {Israel J. Math.}, + FJOURNAL = {Israel Journal of Mathematics}, + VOLUME = {228}, + YEAR = {2018}, + NUMBER = {2}, + PAGES = {587--626}, + ISSN = {0021-2172}, + MRCLASS = {14H37 (12F10)}, + MRNUMBER = {3874854}, +MRREVIEWER = {Valentijn Zo\"{e} Karemaker}, + DOI = {10.1007/s11856-018-1782-1}, + URL = {https://doi.org/10.1007/s11856-018-1782-1}, +} + + + +@misc{OlsonMSRI, +Author = {Martin Olson}, +Title = {Tangent spaces and obstructed theories}, +Year = {2019}, +url = {https://math.berkeley.edu/~molsson/MSRISummer07.pdf}, +} + +@article {MR4333646, + AUTHOR = {Kontogeorgis, Aristides and Terezakis, Alexios and Tsouknidas, + Ioannis}, + TITLE = {Automorphisms and the canonical ideal}, + JOURNAL = {Mediterr. J. Math.}, + FJOURNAL = {Mediterranean Journal of Mathematics}, + VOLUME = {18}, + YEAR = {2021}, + NUMBER = {6}, + PAGES = {Paper No. 261, 15}, + ISSN = {1660-5446}, + MRCLASS = {14H37 (13D02)}, + MRNUMBER = {4333646}, + DOI = {10.1007/s00009-021-01878-3}, + URL = {https://doi.org/10.1007/s00009-021-01878-3}, +} + + +@article {MR4223071, + AUTHOR = {Kontogeorgis, Aristides and Paramantzoglou, Panagiotis}, + TITLE = {A non-commutative differential module approach to {A}lexander + modules}, + JOURNAL = {Forum Math.}, + FJOURNAL = {Forum Mathematicum}, + VOLUME = {33}, + YEAR = {2021}, + NUMBER = {2}, + PAGES = {427--434}, + ISSN = {0933-7741}, + MRCLASS = {57M12 (13N05 14H30 20F34)}, + MRNUMBER = {4223071}, + DOI = {10.1515/forum-2020-0224}, + URL = {https://doi.org/10.1515/forum-2020-0224}, +} + + + +@article {MR4186523, + AUTHOR = {Kontogeorgis, Aristides and Paramantzoglou, Panagiotis}, + TITLE = {Galois action on homology of generalized {F}ermat curves}, + JOURNAL = {Q. J. Math.}, + FJOURNAL = {The Quarterly Journal of Mathematics}, + VOLUME = {71}, + YEAR = {2020}, + NUMBER = {4}, + PAGES = {1377--1417}, + ISSN = {0033-5606}, + MRCLASS = {14H30 (11G30 14G32)}, + MRNUMBER = {4186523}, + DOI = {10.1093/qmath/haaa038}, + URL = {https://doi.org/10.1093/qmath/haaa038}, +} + +@article {MR3827807, + AUTHOR = {Aiello, Valeriano and Conti, Roberto and Jones, Vaughan F. R.}, + TITLE = {The {H}omflypt polynomial and the oriented {T}hompson group}, + JOURNAL = {Quantum Topol.}, + FJOURNAL = {Quantum Topology}, + VOLUME = {9}, + YEAR = {2018}, + NUMBER = {3}, + PAGES = {461--472}, + ISSN = {1663-487X}, + MRCLASS = {57M27 (20F65)}, + MRNUMBER = {3827807}, +MRREVIEWER = {Bruno P. Zimmermann}, + DOI = {10.4171/QT/112}, + URL = {https://doi.org/10.4171/QT/112}, +} + +@book {MR2706280, + AUTHOR = {Belk, James Michael}, + TITLE = {Thompsons' group {F}}, + NOTE = {Thesis (Ph.D.)--Cornell University}, + PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, + YEAR = {2004}, + PAGES = {143}, + ISBN = {978-0496-88011-9}, + MRCLASS = {Thesis}, + MRNUMBER = {2706280}, + URL = + {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3140871}, +} + +@article {MR1396957, + AUTHOR = {Guba, Victor and Sapir, Mark}, + TITLE = {Diagram groups}, + JOURNAL = {Mem. Amer. Math. Soc.}, + FJOURNAL = {Memoirs of the American Mathematical Society}, + VOLUME = {130}, + YEAR = {1997}, + NUMBER = {620}, + PAGES = {viii+117}, + ISSN = {0065-9266}, + MRCLASS = {20F05 (57M07)}, + MRNUMBER = {1396957}, +MRREVIEWER = {Thomas Delzant}, + DOI = {10.1090/memo/0620}, + URL = {https://doi.org/10.1090/memo/0620}, +} + +@incollection {MR4252293, + AUTHOR = {Antoniadis, Jannis A. and Kontogeorgis, Aristides}, + TITLE = {The group of automorphisms of the {H}eisenberg curve}, + BOOKTITLE = {Abelian varieties and number theory}, + SERIES = {Contemp. Math.}, + VOLUME = {767}, + PAGES = {25--39}, + PUBLISHER = {Amer. Math. Soc., [Providence], RI}, + YEAR = {[2021] \copyright 2021}, + MRCLASS = {14H37}, + MRNUMBER = {4252293}, + DOI = {10.1090/conm/767/15395}, + URL = {https://doi.org/10.1090/conm/767/15395}, +} + +@article {MR2577662, + AUTHOR = {Obus, Andrew and Pries, Rachel}, + TITLE = {Wild tame-by-cyclic extensions}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {214}, + YEAR = {2010}, + NUMBER = {5}, + PAGES = {565--573}, + ISSN = {0022-4049}, + MRCLASS = {12F10 (11S15 11S20 14H30)}, + MRNUMBER = {2577662}, +MRREVIEWER = {K. Kiyek}, + DOI = {10.1016/j.jpaa.2009.06.017}, + URL = {https://doi.org/10.1016/j.jpaa.2009.06.017}, +} + +@incollection {MR1082360, + AUTHOR = {Lazarsfeld, Robert}, + TITLE = {A sampling of vector bundle techniques in the study of linear + series}, + BOOKTITLE = {Lectures on {R}iemann surfaces ({T}rieste, 1987)}, + PAGES = {500--559}, + PUBLISHER = {World Sci. Publ., Teaneck, NJ}, + YEAR = {1989}, + MRCLASS = {14C20 (14F05 14H10 14H60 14J28)}, + MRNUMBER = {1082360}, +MRREVIEWER = {Angelo Lopez}, +} + +@article {MR1136544, + AUTHOR = {Ancona, Vincenzo and Ottaviani, Giorgio}, + TITLE = {Stability of special instanton bundles on {${\bf P}^{2n+1}$}}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {341}, + YEAR = {1994}, + NUMBER = {2}, + PAGES = {677--693}, + ISSN = {0002-9947}, + MRCLASS = {14F05}, + MRNUMBER = {1136544}, +MRREVIEWER = {Wolfram Decker}, + DOI = {10.2307/2154578}, + URL = {https://doi.org/10.2307/2154578}, +} + + +@article {MR608528, + AUTHOR = {Taylor, M. J.}, + TITLE = {On {F}r\"{o}hlich's conjecture for rings of integers of tame + extensions}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {63}, + YEAR = {1981}, + NUMBER = {1}, + PAGES = {41--79}, + ISSN = {0020-9910}, + MRCLASS = {12A55 (12A57)}, + MRNUMBER = {608528}, +MRREVIEWER = {Hans Opolka}, + DOI = {10.1007/BF01389193}, + URL = {https://doi.org/10.1007/BF01389193}, +} + +@article {MR728135, + AUTHOR = {Nakajima, S.}, + TITLE = {On {G}alois module structure of the cohomology groups of an + algebraic variety}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {75}, + YEAR = {1984}, + NUMBER = {1}, + PAGES = {1--8}, + ISSN = {0020-9910}, + MRCLASS = {14E20 (14F05)}, + MRNUMBER = {728135}, +MRREVIEWER = {R. T. Hoobler}, + DOI = {10.1007/BF01403086}, + URL = {https://doi.org/10.1007/BF01403086}, +} + +@phdthesis{Pagot, + title = {Rel\`{e}vement en caract\'{e}ristique z\'{e}ro d'actions de groupes ab\'{e}liens de type $(p, \ldots, p)$}, + school = {Universit\'{e} Bordeaux I, available at \url{http://www.math.u-bordeaux1.fr/~mmatigno/Pagot-These.pdf}}, + author = {Guillaume Pagot}, + year = {2002}, +} + +@article {MR849058, + AUTHOR = {Schreyer, Frank-Olaf}, + TITLE = {Syzygies of canonical curves and special linear series}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {275}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {105--137}, + ISSN = {0025-5831}, + MRCLASS = {14H45}, + MRNUMBER = {849058}, +MRREVIEWER = {Joseph Harris}, + DOI = {10.1007/BF01458587}, + URL = {https://doi.org/10.1007/BF01458587}, +} + +@article {MR4022070, + AUTHOR = {Aprodu, Marian and Farkas, Gavril and Papadima, \c{S}tefan and + Raicu, Claudiu and Weyman, Jerzy}, + TITLE = {Koszul modules and {G}reen's conjecture}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {218}, + YEAR = {2019}, + NUMBER = {3}, + PAGES = {657--720}, + ISSN = {0020-9910}, + MRCLASS = {14H51 (13D02 14M15 14N05 20G05)}, + MRNUMBER = {4022070}, +MRREVIEWER = {Yeongrak Kim}, + DOI = {10.1007/s00222-019-00894-1}, + URL = {https://doi.org/10.1007/s00222-019-00894-1}, +} + +@article {MR1753111, + AUTHOR = {Pappas, Georgios}, + TITLE = {Galois module structure and the {$\gamma$}-filtration}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {121}, + YEAR = {2000}, + NUMBER = {1}, + PAGES = {79--104}, + ISSN = {0010-437X}, + MRCLASS = {14F05 (11R33 14C35 19A31 19E08)}, + MRNUMBER = {1753111}, +MRREVIEWER = {Nigel Byott}, + DOI = {10.1023/A:1001722414377}, + URL = {https://doi.org/10.1023/A:1001722414377}, +} + +@incollection {MR1804943, + AUTHOR = {Erez, Boas}, + TITLE = {Galois modules and class field theory}, + BOOKTITLE = {Invitation to higher local fields ({M}\"{u}nster, 1999)}, + SERIES = {Geom. Topol. Monogr.}, + VOLUME = {3}, + PAGES = {299--304}, + PUBLISHER = {Geom. Topol. Publ., Coventry}, + YEAR = {2000}, + MRCLASS = {11R33 (11R37 14G25)}, + MRNUMBER = {1804943}, +MRREVIEWER = {Nigel Byott}, + DOI = {10.2140/gtm.2000.3.299}, + URL = {https://doi.org/10.2140/gtm.2000.3.299}, +} + +@article {MR2552102, + AUTHOR = {Chinburg, Ted and Pappas, Georgios and Taylor, Martin J.}, + TITLE = {Cubic structures, equivariant {E}uler characteristics and + lattices of modular forms}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {170}, + YEAR = {2009}, + NUMBER = {2}, + PAGES = {561--608}, + ISSN = {0003-486X}, + MRCLASS = {14C40 (11G40 14G40 19L10)}, + MRNUMBER = {2552102}, +MRREVIEWER = {Nigel Byott}, + DOI = {10.4007/annals.2009.170.561}, + URL = {https://doi.org/10.4007/annals.2009.170.561}, +} + +@article {MR511812, + AUTHOR = {Cassou-Nogu\`es, Philippe}, + TITLE = {Quelques th\'{e}or\`emes de base normale d'entiers}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {28}, + YEAR = {1978}, + NUMBER = {3}, + PAGES = {ix, 1--33}, + ISSN = {0373-0956}, + MRCLASS = {12B17 (12A57 20C10)}, + MRNUMBER = {511812}, +MRREVIEWER = {Ky\^{u}ya Masuda}, + URL = {http://www.numdam.org/item?id=AIF_1978__28_3_1_0}, +} + +@article {MR1626489, + AUTHOR = {Pappas, Georgios}, + TITLE = {Galois modules and the theorem of the cube}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {133}, + YEAR = {1998}, + NUMBER = {1}, + PAGES = {193--225}, + ISSN = {0020-9910}, + MRCLASS = {11R33 (14C40 14L30)}, + MRNUMBER = {1626489}, +MRREVIEWER = {Nigel Byott}, + DOI = {10.1007/s002220050244}, + URL = {https://doi.org/10.1007/s002220050244}, +} + +@phdthesis{Sugil, + title = {Galois module structure of weakly ramified covers of curves}, + school = {Michigan State University}, + author = {Sugil Lee}, + year = {2020}, +} + +@phdthesis{Wood, + title = {Galois structure of holomorphic polydifferentials in positive characteristic}, + school = {University of Iowa}, + author = {Adam Wood}, + year = {2020}, +} + + +@ARTICLE{zachos2020orthogonal, + author = {{Zachos}, Ioannis}, + title = "{On orthogonal local models of Hodge type}", + journal = {arXiv e-prints}, + keywords = {Mathematics - Algebraic Geometry}, + year = 2020, + month = jun, + eid = {arXiv:2006.07271}, + pages = {arXiv:2006.07271}, +archivePrefix = {arXiv}, + eprint = {2006.07271}, + primaryClass = {math.AG}, + adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200607271Z}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + + + +@ARTICLE{pappas2021regular, + author = {{Pappas}, Georgios and {Zachos}, Ioannis}, + title = "{Regular integral models for Shimura varieties of orthogonal type}", + journal = {arXiv e-prints}, + keywords = {Mathematics - Number Theory, Mathematics - Algebraic Geometry}, + year = 2021, + month = feb, + eid = {arXiv:2102.02687}, + pages = {arXiv:2102.02687}, +archivePrefix = {arXiv}, + eprint = {2102.02687}, + primaryClass = {math.NT}, + adsurl = {https://ui.adsabs.harvard.edu/abs/2021arXiv210202687P}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + + + +@article {MR1030141, + AUTHOR = {Eisenbud, David and Lange, Herbert and Martens, Gerriet and + Schreyer, Frank-Olaf}, + TITLE = {The {C}lifford dimension of a projective curve}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {72}, + YEAR = {1989}, + NUMBER = {2}, + PAGES = {173--204}, + ISSN = {0010-437X}, + MRCLASS = {14H45 (14C20 14J28)}, + MRNUMBER = {1030141}, +MRREVIEWER = {Olivier Debarre}, + URL = {http://www.numdam.org/item?id=CM_1989__72_2_173_0}, +} + +@article {MR813583, + AUTHOR = {Green, Mark and Lazarsfeld, Robert}, + TITLE = {On the projective normality of complete linear series on an + algebraic curve}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {83}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {73--90}, + ISSN = {0020-9910}, + MRCLASS = {14H10 (14H45)}, + MRNUMBER = {813583}, +MRREVIEWER = {H. Lange}, + DOI = {10.1007/BF01388754}, + URL = {https://doi.org/10.1007/BF01388754}, +} + +@book {MR717033, + AUTHOR = {Fr\"{o}hlich, Albrecht}, + TITLE = {Galois module structure of algebraic integers}, + SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results + in Mathematics and Related Areas (3)]}, + VOLUME = {1}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1983}, + PAGES = {x+262}, + ISBN = {3-540-11920-5}, + MRCLASS = {11R33 (11R32 11R65)}, + MRNUMBER = {717033}, +MRREVIEWER = {Jerzy Browkin}, + DOI = {10.1007/978-3-642-68816-4}, + URL = {https://doi.org/10.1007/978-3-642-68816-4}, +} + +@article {MR1128708, + AUTHOR = {Erez, B.}, + TITLE = {The {G}alois structure of the square root of the inverse + different}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {208}, + YEAR = {1991}, + NUMBER = {2}, + PAGES = {239--255}, + ISSN = {0025-5874}, + MRCLASS = {11R33 (11R32)}, + MRNUMBER = {1128708}, +MRREVIEWER = {J\"{u}rgen Ritter}, + DOI = {10.1007/BF02571523}, + URL = {https://doi.org/10.1007/BF02571523}, +} + +@book {SGA1, + AUTHOR = {Grothendieck, Alexander}, + TITLE = {Rev\^{e}tements \'{e}tales et groupe fondamental. {F}asc. {I}: + {E}xpos\'{e}s 1 \`a 5}, + SERIES = {S\'{e}minaire de G\'{e}om\'{e}trie Alg\'{e}brique}, + VOLUME = {1960/61}, + PUBLISHER = {Institut des Hautes \'{E}tudes Scientifiques, Paris}, + YEAR = {1963}, + PAGES = {iv+143 pp. (not consecutively paged) (loose errata)}, + MRCLASS = {14.55}, + MRNUMBER = {0217087}, +} + +@misc{SGA1a, +Author = {Alexander Grothendieck and Michele Raynaud}, +Title = {Revêtements étales et groupe fondamental (SGA 1)}, +Year = {2002}, +Eprint = {arXiv:math/0206203}, +} + +@article {MR2254623, + AUTHOR = {Bouw, Irene I. and Wewers, Stefan}, + TITLE = {The local lifting problem for dihedral groups}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {134}, + YEAR = {2006}, + NUMBER = {3}, + PAGES = {421--452}, + ISSN = {0012-7094}, + MRCLASS = {14H37 (11G20 14D15)}, + MRNUMBER = {2254623}, +MRREVIEWER = {Marko Roczen}, + DOI = {10.1215/S0012-7094-06-13431-2}, + URL = {https://doi.org/10.1215/S0012-7094-06-13431-2}, +} + +@article {MR2534115, + AUTHOR = {Brewis, Louis Hugo and Wewers, Stefan}, + TITLE = {Artin characters, {H}urwitz trees and the lifting problem}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {345}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {711--730}, + ISSN = {0025-5831}, + MRCLASS = {14G20 (11S31 13F25 14H30 14H37 14L30)}, + MRNUMBER = {2534115}, +MRREVIEWER = {Daniel Barsky}, + DOI = {10.1007/s00208-009-0374-0}, + URL = {https://doi.org/10.1007/s00208-009-0374-0}, +} + +@article {MR3069638, + AUTHOR = {Chevalley, C. and Weil, A. and Hecke, E.}, + TITLE = {\"{U}ber das verhalten der integrale 1. gattung bei automorphismen + des funktionenk\"{o}rpers}, + JOURNAL = {Abh. Math. Sem. Univ. Hamburg}, + FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t + Hamburg}, + VOLUME = {10}, + YEAR = {1934}, + NUMBER = {1}, + PAGES = {358--361}, + ISSN = {0025-5858}, + MRCLASS = {DML}, + MRNUMBER = {3069638}, + DOI = {10.1007/BF02940687}, + URL = {https://doi.org/10.1007/BF02940687}, +} + + + + + + +@book {MR506881, + AUTHOR = {Hazewinkel, Michiel}, + TITLE = {Formal groups and applications}, + SERIES = {Pure and Applied Mathematics}, + VOLUME = {78}, + PUBLISHER = {Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], + New York-London}, + YEAR = {1978}, + PAGES = {xxii+573pp}, + ISBN = {0-12-335150-2}, + MRCLASS = {14L05 (10D30 12B25 55N22)}, + MRNUMBER = {506881}, +MRREVIEWER = {Robert A. Morris}, +} + +@article {MR3556796, + AUTHOR = {Obus, Andrew}, + TITLE = {The local lifting problem for {$A_4$}}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {10}, + YEAR = {2016}, + NUMBER = {8}, + PAGES = {1683--1693}, + ISSN = {1937-0652}, + MRCLASS = {14H37 (12F10 13B05 14B12)}, + MRNUMBER = {3556796}, +MRREVIEWER = {Marko Roczen}, + DOI = {10.2140/ant.2016.10.1683}, + URL = {https://doi.org/10.2140/ant.2016.10.1683}, +} + + +@article {MR2525558, + AUTHOR = {Himstedt, Frank and Symonds, Peter}, + TITLE = {Equivariant {H}ilbert series}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {3}, + YEAR = {2009}, + NUMBER = {4}, + PAGES = {423--443}, + ISSN = {1937-0652}, + MRCLASS = {13D40 (20C20)}, + MRNUMBER = {2525558}, +MRREVIEWER = {Adam L. Van Tuyl}, + DOI = {10.2140/ant.2009.3.423}, + URL = {https://doi.org/10.2140/ant.2009.3.423}, +} + +@article {MR1274097, + AUTHOR = {Chinburg, Ted}, + TITLE = {Galois structure of de {R}ham cohomology of tame covers of + schemes}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {139}, + YEAR = {1994}, + NUMBER = {2}, + PAGES = {443--490}, + ISSN = {0003-486X}, + MRCLASS = {11R33 (14F40 14G10)}, + MRNUMBER = {1274097}, +MRREVIEWER = {Boas Erez}, + DOI = {10.2307/2946586}, + URL = {https://doi.org/10.2307/2946586}, +} + +@article{Chinburg1996TameAO, + title={Tame actions of group schemes: integrals and slices}, + author={T. Chinburg and B. Erez and G. Pappas and M. Taylor}, + journal={Duke Mathematical Journal}, + year={1996}, + volume={82}, + pages={269-308} +} + +@article {MR3874854, + AUTHOR = {Weaver, Bradley}, + TITLE = {The local lifting problem for {$D_4$}}, + JOURNAL = {Israel J. Math.}, + FJOURNAL = {Israel Journal of Mathematics}, + VOLUME = {228}, + YEAR = {2018}, + NUMBER = {2}, + PAGES = {587--626}, + ISSN = {0021-2172}, + MRCLASS = {14H37 (12F10)}, + MRNUMBER = {3874854}, +MRREVIEWER = {Valentijn Zo\"{e} Karemaker}, + DOI = {10.1007/s11856-018-1782-1}, + URL = {https://doi.org/10.1007/s11856-018-1782-1}, +} + +@book {MR2868112, + AUTHOR = {Stanley, Richard P.}, + TITLE = {Enumerative combinatorics. {V}olume 1}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {49}, + EDITION = {Second}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2012}, + PAGES = {xiv+626}, + ISBN = {978-1-107-60262-5}, + MRCLASS = {05-02 (05A15 06-02)}, + MRNUMBER = {2868112}, +} + +@book {MR1251956, + AUTHOR = {Bruns, Winfried and Herzog, J\"{u}rgen}, + TITLE = {Cohen-{M}acaulay rings}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {39}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1993}, + PAGES = {xii+403}, + ISBN = {0-521-41068-1}, + MRCLASS = {13H10 (13-02)}, + MRNUMBER = {1251956}, +MRREVIEWER = {Matthew Miller}, +} + +@inproceedings{10.1145/3373207.3404046, +author = {Charalambous, Hara and Karagiannis, Kostas and Karanikolopoulos, Sotiris and Kontogeorgis, Aristides}, +title = {Syzygies of Ideals of Polynomial Rings over Principal Ideal Domains}, +year = {2020}, +isbn = {9781450371001}, +publisher = {Association for Computing Machinery}, +address = {New York, NY, USA}, + +url = {https://doi.org/10.1145/3373207.3404046}, +doi = {10.1145/3373207.3404046}, +abstract = {We study computational aspects of syzygies of graded modules over polynomial rings R[w1, ..., wg] when the base R is a discrete valuation ring. In particular, we use the torsion of their syzygies over R to provide a formula which describes the behavior of the Betti numbers when changing the base to the residue field or the fraction field of R. Our work is motivated by the deformation theory of curves.}, +booktitle = {Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation}, +pages = {78–82}, +numpages = {5}, +keywords = {lifting MSC:13D02, 13P20, principal ideal domains, syzygies, commutive algebra, reduction}, +location = {Kalamata, Greece}, +series = {ISSAC '20} +} + +@article {MR4302549, + AUTHOR = {Dokchitser, Tim}, + TITLE = {Models of curves over discrete valuation rings}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {170}, + YEAR = {2021}, + NUMBER = {11}, + PAGES = {2519--2574}, + ISSN = {0012-7094}, + MRCLASS = {11G20 (11G10 14D10 14F20 14H45)}, + MRNUMBER = {4302549}, +MRREVIEWER = {J\polhk edrzej Garnek}, + DOI = {10.1215/00127094-2020-0079}, + URL = {https://doi.org/10.1215/00127094-2020-0079}, +} + +@ARTICLE{charalambous2019relative, + author = {{Charalambous}, Hara and {Karagiannis}, Kostas and {Kontogeorgis}, Aristides}, + title = "{The Relative Canonical Ideal of the Artin-Schreier-Kummer-Witt family of curves}", + journal = {arXiv e-prints}, + keywords = {Mathematics - Algebraic Geometry, Mathematics - Number Theory, 14F10, 14H37, 14H10, 14G17, 14G20, 14D15, 11G20}, + year = 2019, + + month = may, + eid = {arXiv:1905.05545}, + pages = {arXiv:1905.05545}, +archivePrefix = {arXiv}, + eprint = {1905.05545}, + primaryClass = {math.AG}, + adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190505545C}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + + + + +@article {MR4194180, + AUTHOR = {Kontogeorgis, Aristides and Tsouknidas, Ioannis}, + TITLE = {A generating set for the canonical ideal of {HKG}-curves}, + JOURNAL = {Res. Number Theory}, + FJOURNAL = {Research in Number Theory}, + VOLUME = {7}, + YEAR = {2021}, + NUMBER = {1}, + PAGES = {Paper No. 4, 16}, + ISSN = {2522-0160}, + MRCLASS = {14H55}, + MRNUMBER = {4194180}, + DOI = {10.1007/s40993-020-00230-0}, + URL = {https://doi.org/10.1007/s40993-020-00230-0}, +} + +@article {MR1818984, + AUTHOR = {Bondal, Alexei and Orlov, Dmitri}, + TITLE = {Reconstruction of a variety from the derived category and + groups of autoequivalences}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {125}, + YEAR = {2001}, + NUMBER = {3}, + PAGES = {327--344}, + ISSN = {0010-437X}, + MRCLASS = {18E30 (14F05)}, + MRNUMBER = {1818984}, +MRREVIEWER = {Richard P. Thomas}, + DOI = {10.1023/A:1002470302976}, + URL = {https://doi.org/10.1023/A:1002470302976}, +} + + +@inproceedings {MR1403918, + AUTHOR = {Kontsevich, Maxim}, + TITLE = {Homological algebra of mirror symmetry}, + BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of + {M}athematicians, {V}ol. 1, 2 ({Z}\"{u}rich, 1994)}, + PAGES = {120--139}, + PUBLISHER = {Birkh\"{a}user, Basel}, + YEAR = {1995}, + MRCLASS = {32J25 (14D07 14J32 18E30 32G05)}, + MRNUMBER = {1403918}, +MRREVIEWER = {Claire Voisin}, +} + +@article {MR1831820, + AUTHOR = {Seidel, Paul and Thomas, Richard}, + TITLE = {Braid group actions on derived categories of coherent sheaves}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {108}, + YEAR = {2001}, + NUMBER = {1}, + PAGES = {37--108}, + ISSN = {0012-7094}, + MRCLASS = {14F05 (14J32 18E30 20F36 53D40)}, + MRNUMBER = {1831820}, +MRREVIEWER = {Mikhail G. Khovanov}, + DOI = {10.1215/S0012-7094-01-10812-0}, + URL = {https://doi.org/10.1215/S0012-7094-01-10812-0}, +} + + +@article {MR762512, + AUTHOR = {Goldman, William M.}, + TITLE = {The symplectic nature of fundamental groups of surfaces}, + JOURNAL = {Adv. in Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {54}, + YEAR = {1984}, + NUMBER = {2}, + PAGES = {200--225}, + ISSN = {0001-8708}, + MRCLASS = {32G15 (57M05)}, + MRNUMBER = {762512}, +MRREVIEWER = {C. Earle}, + DOI = {10.1016/0001-8708(84)90040-9}, + URL = {https://doi.org/10.1016/0001-8708(84)90040-9}, +} + +@article {MR4271484, + AUTHOR = {Pappas, Georgios}, + TITLE = {Volume and symplectic structure for {$\ell$}-adic local + systems}, + JOURNAL = {Adv. Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {387}, + YEAR = {2021}, + PAGES = {Paper No. 107836, 70}, + ISSN = {0001-8708}, + MRCLASS = {14G22 (11F80 14F20 19F27)}, + MRNUMBER = {4271484}, + DOI = {10.1016/j.aim.2021.107836}, + URL = {https://doi.org/10.1016/j.aim.2021.107836}, +} + + +@misc{https://doi.org/10.48550/arxiv.2101.11084, + doi = {10.48550/ARXIV.2101.11084}, + + url = {https://arxiv.org/abs/2101.11084}, + + author = {Kontogeorgis, Aristides and Terezakis, Alexios}, + + keywords = {Algebraic Geometry (math.AG), FOS: Mathematics, FOS: Mathematics, 14H37, 14D15, 14H10, 13D02}, + + title = {The canonical ideal and the deformation theory of curves with automorphisms}, + + publisher = {arXiv}, + + year = {2021}, + + copyright = {Creative Commons Attribution 4.0 International} +} + + +@book {MR1915966, + AUTHOR = {Fesenko, I. B. and Vostokov, S. V.}, + TITLE = {Local fields and their extensions}, + SERIES = {Translations of Mathematical Monographs}, + VOLUME = {121}, + EDITION = {Second}, + NOTE = {With a foreword by I. R. Shafarevich}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2002}, + PAGES = {xii+345}, + ISBN = {0-8218-3259-X}, + MRCLASS = {11Sxx (11S31)}, + MRNUMBER = {1915966}, +MRREVIEWER = {Jerzy Browkin}, + DOI = {10.1090/mmono/121}, + URL = {https://doi.org/10.1090/mmono/121}, +} + +@incollection {MR2484083, + AUTHOR = {Wedhorn, Torsten}, + TITLE = {De {R}ham cohomology of varieties over fields of positive + characteristic}, + BOOKTITLE = {Higher-dimensional geometry over finite fields}, + SERIES = {NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur.}, + VOLUME = {16}, + PAGES = {269--314}, + PUBLISHER = {IOS, Amsterdam}, + YEAR = {2008}, + MRCLASS = {14F40 (14J28)}, + MRNUMBER = {2484083}, +} + +@article {MR1477762, + AUTHOR = {Chinburg, Ted and Erez, Boas and Pappas, Georgios and Taylor, + Martin J.}, + TITLE = {{$\epsilon$}-constants and the {G}alois structure of de {R}ham + cohomology}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {146}, + YEAR = {1997}, + NUMBER = {2}, + PAGES = {411--473}, + ISSN = {0003-486X}, + MRCLASS = {14F40 (11G09 11R33)}, + MRNUMBER = {1477762}, +MRREVIEWER = {Nigel Byott}, + DOI = {10.2307/2952466}, + URL = {https://doi.org/10.2307/2952466}, +} + +@article {MR1274097, + AUTHOR = {Chinburg, Ted}, + TITLE = {Galois structure of de {R}ham cohomology of tame covers of + schemes}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {139}, + YEAR = {1994}, + NUMBER = {2}, + PAGES = {443--490}, + ISSN = {0003-486X}, + MRCLASS = {11R33 (14F40 14G10)}, + MRNUMBER = {1274097}, +MRREVIEWER = {Boas Erez}, + DOI = {10.2307/2946586}, + URL = {https://doi.org/10.2307/2946586}, +} + +@article {MR1183915, + AUTHOR = {Chinburg, Ted}, + TITLE = {Galois structure of de {R}ham cohomology}, + JOURNAL = {S\'{e}m. Th\'{e}or. Nombres Bordeaux (2)}, + FJOURNAL = {S\'{e}minaire de Th\'{e}orie des Nombres de Bordeaux. S\'{e}rie 2}, + VOLUME = {4}, + YEAR = {1992}, + NUMBER = {1}, + PAGES = {1--18}, + ISSN = {0989-5558}, + MRCLASS = {14F40 (14E20 14G15)}, + MRNUMBER = {1183915}, +MRREVIEWER = {G. Horrocks}, + URL = {http://jtnb.cedram.org/item?id=JTNB_1992__4_1_1_0}, +} + +@article {MR453885, + AUTHOR = {Lusztig, G.}, + TITLE = {Coxeter orbits and eigenspaces of {F}robenius}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {38}, + YEAR = {1976/77}, + NUMBER = {2}, + PAGES = {101--159}, + ISSN = {0020-9910}, + MRCLASS = {20G05}, + MRNUMBER = {453885}, +MRREVIEWER = {David Kazhdan}, + DOI = {10.1007/BF01408569}, + URL = {https://doi.org/10.1007/BF01408569}, +} + +@article {MR1723124, + AUTHOR = {Dummigan, Neil}, + TITLE = {Complete {$p$}-descent for {J}acobians of {H}ermitian curves}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {119}, + YEAR = {1999}, + NUMBER = {2}, + PAGES = {111--132}, + ISSN = {0010-437X}, + MRCLASS = {11G20 (11G10 11G30 11G40 14F30)}, + MRNUMBER = {1723124}, +MRREVIEWER = {Massimo Bertolini}, + DOI = {10.1023/A:1001721808335}, + URL = {https://doi.org/10.1023/A:1001721808335}, +} + +@article {MR1320616, + AUTHOR = {Liu, Li-Qian}, + TITLE = {The decomposition numbers of {${\rm Suz}(q)$}}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {172}, + YEAR = {1995}, + NUMBER = {1}, + PAGES = {1--31}, + ISSN = {0021-8693}, + MRCLASS = {20C34 (20C20)}, + MRNUMBER = {1320616}, +MRREVIEWER = {Leonard Chastkofsky}, + DOI = {10.1006/jabr.1995.1045}, + URL = {https://doi.org/10.1006/jabr.1995.1045}, +} + +@article {MR3782449, + AUTHOR = {K\"{o}ck, Bernhard and Tait, Joseph}, + TITLE = {On the de-{R}ham cohomology of hyperelliptic curves}, + JOURNAL = {Res. Number Theory}, + FJOURNAL = {Research in Number Theory}, + VOLUME = {4}, + YEAR = {2018}, + NUMBER = {2}, + PAGES = {Paper No. 19, 17}, + ISSN = {2522-0160}, + MRCLASS = {14F40 (14G17 14H37)}, + MRNUMBER = {3782449}, +MRREVIEWER = {Nobuo Tsuzuki}, + DOI = {10.1007/s40993-018-0111-4}, + URL = {https://doi.org/10.1007/s40993-018-0111-4}, +} + +@article {MR3007205, + AUTHOR = {Hortsch, Ruthi}, + TITLE = {On the canonical representation of curves in positive + characteristic}, + JOURNAL = {New York J. Math.}, + FJOURNAL = {New York Journal of Mathematics}, + VOLUME = {18}, + YEAR = {2012}, + PAGES = {911--924}, + MRCLASS = {14G17 (11G05)}, + MRNUMBER = {3007205}, +MRREVIEWER = {Rachel J. Pries}, + URL = {http://nyjm.albany.edu:8000/j/2012/18_911.html}, +} + + + + +@book {MR4225278, + AUTHOR = {G\"{o}rtz, Ulrich and Wedhorn, Torsten}, + TITLE = {Algebraic geometry {I}. {S}chemes---with examples and + exercises}, + SERIES = {Springer Studium Mathematik---Master}, + NOTE = {Second edition [of 2675155]}, + PUBLISHER = {Springer Spektrum, Wiesbaden}, + YEAR = {[2020] \copyright 2020}, + PAGES = {vii+625}, + ISBN = {978-3-658-30732-5; 978-3-658-30733-2}, + MRCLASS = {14-01}, + MRNUMBER = {4225278}, + DOI = {10.1007/978-3-658-30733-2}, + URL = {https://doi.org/10.1007/978-3-658-30733-2}, +} + +@misc{https://doi.org/10.48550/arxiv.2301.01032, + doi = {10.48550/ARXIV.2301.01032}, + + url = {https://arxiv.org/abs/2301.01032}, + + author = {Kontogeorgis, Aristides and Terezakis, Alexios}, + + keywords = {Algebraic Geometry (math.AG), Representation Theory (math.RT), FOS: Mathematics, FOS: Mathematics, 20C20, 20C10, 14H37}, + + title = {On the lifting problem of representations of a metacyclic group}, + + publisher = {arXiv}, + + year = {2023}, + + copyright = {Creative Commons Attribution 4.0 International} +} + +@article {MR4779377, + AUTHOR = {Kontogeorgis, Aristides and Terezakis, Alexios}, + TITLE = {On the lifting problem of representations of a metacyclic + group}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {659}, + YEAR = {2024}, + PAGES = {745--779}, + ISSN = {0021-8693,1090-266X}, + MRCLASS = {20C20 (14H37 20C10)}, + MRNUMBER = {4779377}, + DOI = {10.1016/j.jalgebra.2024.07.003}, + URL = {https://doi.org/10.1016/j.jalgebra.2024.07.003}, +} + +@book {MR3408060, + AUTHOR = {Lakshmibai, V. and Brown, Justin}, + TITLE = {The {G}rassmannian variety}, + SERIES = {Developments in Mathematics}, + VOLUME = {42}, + NOTE = {Geometric and representation-theoretic aspects}, + PUBLISHER = {Springer, New York}, + YEAR = {2015}, + PAGES = {x+172}, + ISBN = {978-1-4939-3081-4; 978-1-4939-3082-1}, + MRCLASS = {14M15 (13P10 14M12)}, + MRNUMBER = {3408060}, +MRREVIEWER = {Li Li}, + DOI = {10.1007/978-1-4939-3082-1}, + URL = {https://doi.org/10.1007/978-1-4939-3082-1}, +} + +@manual{sagemath9.8, + Key = {SageMath}, + Author = {{The Sage Developers}}, + Title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 9.8)}, + note = {{\tt https://www.sagemath.org}}, + Year = {2023}, +} + +@book {MR2244106, + AUTHOR = {Huybrechts, D.}, + TITLE = {Fourier-{M}ukai transforms in algebraic geometry}, + SERIES = {Oxford Mathematical Monographs}, + PUBLISHER = {The Clarendon Press, Oxford University Press, Oxford}, + YEAR = {2006}, + PAGES = {viii+307}, + ISBN = {978-0-19-929686-6; 0-19-929686-3}, + MRCLASS = {14F05 (14-02 18E30)}, + MRNUMBER = {2244106}, +MRREVIEWER = {Bal\'{a}zs Szendr\H{o}i}, + DOI = {10.1093/acprof:oso/9780199296866.001.0001}, + URL = {https://doi.org/10.1093/acprof:oso/9780199296866.001.0001}, +} + +@article {MR124328, + AUTHOR = {Mumford, David}, + TITLE = {Pathologies of modular algebraic surfaces}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {83}, + YEAR = {1961}, + PAGES = {339--342}, + ISSN = {0002-9327}, + MRCLASS = {14.20}, + MRNUMBER = {124328}, +MRREVIEWER = {M. Rosenlicht}, + DOI = {10.2307/2372959}, + URL = {https://doi.org/10.2307/2372959}, +} + +@article {MR894379, + AUTHOR = {Deligne, Pierre and Illusie, Luc}, + TITLE = {Rel\`evements modulo {$p^2$} et d\'{e}composition du complexe de de + {R}ham}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {89}, + YEAR = {1987}, + NUMBER = {2}, + PAGES = {247--270}, + ISSN = {0020-9910}, + MRCLASS = {14F40 (14C30)}, + MRNUMBER = {894379}, +MRREVIEWER = {Thomas Zink}, + DOI = {10.1007/BF01389078}, + URL = {https://doi.org/10.1007/BF01389078}, +} + +@article {MR4363802, + AUTHOR = {Garnek, Jedrzej}, + TITLE = {Equivariant splitting of the {H}odge--de {R}ham exact + sequence}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {300}, + YEAR = {2022}, + NUMBER = {2}, + PAGES = {1917--1938}, + ISSN = {0025-5874}, + MRCLASS = {14F40 (14G17 14H37)}, + MRNUMBER = {4363802}, +MRREVIEWER = {Zijian Zhou}, + DOI = {10.1007/s00209-021-02839-y}, + URL = {https://doi.org/10.1007/s00209-021-02839-y}, +} + +@article {MR349747, + AUTHOR = {Auslander, Maurice}, + TITLE = {Representation theory of {A}rtin algebras. {I}, {II}}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {1}, + YEAR = {1974}, + PAGES = {177--268; ibid. 1 (1974), 269--310}, + ISSN = {0092-7872}, + MRCLASS = {16A46 (18G05)}, + MRNUMBER = {349747}, +MRREVIEWER = {S. S. Page}, + DOI = {10.1080/00927877408548230}, + URL = {https://doi.org/10.1080/00927877408548230}, +} + + + +@article {MR4450616, + AUTHOR = {Dang, Huy and Das, Soumyadip and Karagiannis, Kostas and Obus, + Andrew and Thatte, Vaidehee}, + TITLE = {Local {O}ort groups and the isolated differential data + criterion}, + JOURNAL = {J. Th\'{e}or. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'{e}orie des Nombres de Bordeaux}, + VOLUME = {34}, + YEAR = {2022}, + NUMBER = {1}, + PAGES = {251--269}, + ISSN = {1246-7405,2118-8572}, + MRCLASS = {14H37 (12F10 13B05)}, + MRNUMBER = {4450616}, +MRREVIEWER = {Kevin\ P.\ Keating}, + DOI = {10.5802/jtnb.120}, + URL = {https://doi.org/10.5802/jtnb.120}, +} + + +@book {MartinAigner, + AUTHOR = {Aigner, Martin and G\"unter, Ziegler}, + TITLE = {Αποδείξεις από ΤΟ ΒΙΒΛΙΟ}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Πανεπιστημιακές Εκδόσεις Κρήτης}, + YEAR = {2023}, + PAGES = {313}, + ISBN = {978-960-524-988-5}, +} + + +@book {Pragmatiki, + AUTHOR = {Ανούσης, Μιχάλης and Τσολομύτης, Αντώνης and Φελουζής, Βαγγέλης}, + TITLE = {Πραγματική Ανάλυση}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Ιδιωτική Έκδοση}, + YEAR = {2014}, + PAGES = {198}, + ISBN = {978-960-93-5913-9}, +} + +@book {Elements, + AUTHOR = {Ροκόπανος, Νίκος and Σακελλάρη, Στέλλα and Τσολομύτης, Αντώνης}, + TITLE = {Στοιχεία Ευκλείδου του Αλεξανδρέως}, + SERIES = {}, + NOTE = {}, + PUBLISHER = {Ιδιωτική Έκδοση}, + YEAR = {2021-2022}, + PAGES = {789}, + URL = {https://myria.math.aegean.gr/elements/Stoixeia.pdf}, +} + + + +@article {MR1083613, + AUTHOR = {Kuhn, Stephen}, + TITLE = {The derivative \`a la {C}arath\'{e}odory}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {98}, + YEAR = {1991}, + NUMBER = {1}, + PAGES = {40--44}, + ISSN = {0002-9890,1930-0972}, + MRCLASS = {26A24}, + MRNUMBER = {1083613}, + DOI = {10.2307/2324035}, + URL = {https://doi.org/10.2307/2324035}, +} + + +@article {MR2001152, + AUTHOR = {Derksen, Harm}, + TITLE = {The fundamental theorem of algebra and linear algebra}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {110}, + YEAR = {2003}, + NUMBER = {7}, + PAGES = {620--623}, + ISSN = {0002-9890,1930-0972}, + MRCLASS = {12D10}, + MRNUMBER = {2001152}, + DOI = {10.2307/3647746}, + URL = {https://doi.org/10.2307/3647746}, +} + + +@misc{ConradAlgebra, + author = "Keith Conrad", + title = "The Fundamental Theorem of Algebra", + url = "https://kconrad.math.uconn.edu/blurbs/fundthmalg/fundthmalglinear.pdf" +} + +@article {MR1573476, + AUTHOR = {Kalman, Dan}, + TITLE = {A {M}atrix {P}roof of {N}ewton's {I}dentities}, + JOURNAL = {Math. Mag.}, + FJOURNAL = {Mathematics Magazine}, + VOLUME = {73}, + YEAR = {2000}, + NUMBER = {4}, + PAGES = {313--315}, + ISSN = {0025-570X,1930-0980}, + MRCLASS = {99-04}, + MRNUMBER = {1573476}, + URL = {http://www.jstor.org/stable/2690982?origin=pubexport}, +} + + +@article {MR4317390, + AUTHOR = {Cairns, Hannah}, + TITLE = {Perron's theorem in an hour}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {128}, + YEAR = {2021}, + NUMBER = {8}, + PAGES = {748--752}, + ISSN = {0002-9890,1930-0972}, + MRCLASS = {15B48 (15A18)}, + MRNUMBER = {4317390}, +MRREVIEWER = {Carlos\ Mariju\'{a}n}, + DOI = {10.1080/00029890.2021.1944755}, + URL = {https://doi.org/10.1080/00029890.2021.1944755}, +} + +@misc{Khim, + author = "Suyeon, Khim", + title = "The Frobenius-Perron theorem", + url = "https://www.math.uchicago.edu/~may/VIGRE/VIGRE2007/REUPapers/FINALAPP/Khim.pdf" +} + +@masterthesis{Asterios, + author = {Γκαντζουνης, Αστέριος}, + title = {Η $\zeta$-συνάρτηση του Ihara}, + school = {Μαθηματικό Τμήμα ΕΚΠΑ}, + year = {2013}, + note = {Μεταπτυχιακή εργασία}, + url ={http://users.uoa.gr/~kontogar/students/Gkatzounhs/ptyxiakn.pdf} +} + + +@article {MR1270957, + AUTHOR = {Acosta G., Ernesto and Delgado G., Cesar}, + TITLE = {Fr\'{e}chet vs. {C}arath\'{e}odory}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {101}, + YEAR = {1994}, + NUMBER = {4}, + PAGES = {332--338}, + ISSN = {0002-9890,1930-0972}, + MRCLASS = {26B05 (26A24)}, + MRNUMBER = {1270957}, +MRREVIEWER = {W.\ T.\ Whitley}, + DOI = {10.2307/2975625}, + URL = {https://doi.org/10.2307/2975625}, +} + +@book{pixor, + author = "Πηχωρίδης, Στέλιος", + title = "Απειροστικός Λογισμός, Πρόχειρες Σημειώσεις", + url = "http://users.uoa.gr/~kontogar/notes/ApeirostikosLogismos-SPixwridis.pdf" +} + +@misc{kontogeorgis2023new, + title={An obstruction to the local lifting problem}, + author={Aristides Kontogeorgis and Alexios Terezakis}, + year={2023}, + eprint={2304.08377}, + archivePrefix={arXiv}, + primaryClass={math.AG} +} + + +@misc{dang2023moduli, + title={The moduli space of cyclic covers in positive characteristic}, + author={Huy Dang and Matthias Hippold}, + year={2023}, + eprint={2306.14711}, + archivePrefix={arXiv}, + primaryClass={math.AG} +} + +@article {MR0162799, + AUTHOR = {Baily, Jr., Walter L.}, + TITLE = {On the theory of {$\theta $}-functions, the moduli of abelian + varieties, and the moduli of curves}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {75}, + YEAR = {1962}, + PAGES = {342--381}, + ISSN = {0003-486X}, + MRCLASS = {14.51 (14.20)}, + MRNUMBER = {162799}, +MRREVIEWER = {R.\ C.\ Gunning}, + DOI = {10.2307/1970178}, + URL = {https://doi.org/10.2307/1970178}, +} + +@article {MR0815360, + AUTHOR = {Gessel, Ira and Viennot, G\'{e}rard}, + TITLE = {Binomial determinants, paths, and hook length formulae}, + JOURNAL = {Adv. in Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {58}, + YEAR = {1985}, + NUMBER = {3}, + PAGES = {300--321}, + ISSN = {0001-8708}, + MRCLASS = {05A15 (05A19)}, + MRNUMBER = {815360}, +MRREVIEWER = {S.\ Milne}, + DOI = {10.1016/0001-8708(85)90121-5}, + URL = {https://doi.org/10.1016/0001-8708(85)90121-5}, +} +@book {MR1410264, + AUTHOR = {Morandi, Patrick}, + TITLE = {Field and {G}alois theory}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {167}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1996}, + PAGES = {xvi+281}, + ISBN = {0-387-94753-1}, + MRCLASS = {12-01 (12Fxx)}, + MRNUMBER = {1410264}, +MRREVIEWER = {Martin\ Epkenhans}, + DOI = {10.1007/978-1-4612-4040-2}, + URL = {https://doi.org/10.1007/978-1-4612-4040-2}, +} + +@MISC {152738, + TITLE = {The fibre product of two quotient stacks}, + AUTHOR = {Dori Bejleri (https://mathoverflow.net/users/12402/dori-bejleri)}, + HOWPUBLISHED = {MathOverflow}, + NOTE = {URL:https://mathoverflow.net/q/152738 (version: 2013-12-24)}, + EPRINT = {https://mathoverflow.net/q/152738}, + URL = {https://mathoverflow.net/q/152738} +} + +@article {MR1816711, + AUTHOR = {Biss, Daniel K. and Dasgupta, Samit}, + TITLE = {A presentation for the unipotent group over rings with + identity}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {237}, + YEAR = {2001}, + NUMBER = {2}, + PAGES = {691--707}, + ISSN = {0021-8693,1090-266X}, + MRCLASS = {20H25}, + MRNUMBER = {1816711}, + DOI = {10.1006/jabr.2000.8604}, + URL = {https://doi.org/10.1006/jabr.2000.8604}, +} + +@article {MR1835586, + AUTHOR = {Grassberger, Johannes and H\"ormann, G\"unther}, + TITLE = {A note on representations of the finite {H}eisenberg group and + sums of greatest common divisors}, + JOURNAL = {Discrete Math. Theor. Comput. Sci.}, + FJOURNAL = {Discrete Mathematics \& Theoretical Computer Science. DMTCS. + An Electronic Journal}, + VOLUME = {4}, + YEAR = {2001}, + NUMBER = {2}, + PAGES = {91--100}, + ISSN = {1365-8050}, + MRCLASS = {22E27}, + MRNUMBER = {1835586}, +} + +@book {MR2035696, + AUTHOR = {Adem, Alejandro and Milgram, R. 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a/article_de_rham_cyclic.tex +++ b/article_de_rham_cyclic.tex @@ -411,15 +411,15 @@ shows that $m_{\sigma - 1}$ is well-defined and injective. If $\dim_k \mc T^i M = \dim_k \mc T^{i+1} M$ for some $i$ then: % \[ - \dim_k T^{pi + p} M = \dim_k T^{pi + p - 1} M = \ldots = \dim_k T^{pi - p + 1} M. + \dim_k T^{pi + p} M = \dim_k T^{pi + p - 1} M = \cdots = \dim_k T^{pi - p + 1} M. \] \end{Lemma} \begin{proof} Note that $\mc T^i M = M^{(pi)}/M^{(pi - p)}$. This easily implies that: % \begin{align*} - \dim_k \mc T^i M &= \dim_k T^{pi} M + \ldots + \dim_k T^{pi - p + 1} M\\ - &\ge \dim_k T^{pi+p} M + \ldots + \dim_k T^{pi+1} M + \dim_k \mc T^i M &= \dim_k T^{pi} M + \cdots + \dim_k T^{pi - p + 1} M\\ + &\ge \dim_k T^{pi+p} M + \cdots + \dim_k T^{pi+1} M = \dim_k \mc T^{i+1} M. \end{align*} % @@ -442,11 +442,11 @@ shows that $m_{\sigma - 1}$ is well-defined and injective. $u_{X/Y, Q} = u_{X/Y', Q'}$ for all $p$ points $Q' \in Y'(k)$ in the preimage of $Q$ and: % \begin{equation} \label{eqn:Q_not_in_B'} - p \cdot (u_{X/Y, Q} - 1) = \sum_{Q'} (u_{X/Y', Q'} - 1). + p \cdot (u_{X/Y, Q} - 1) = \sum_{Q' \in {\color{red} \phi^{-1}(Q)}} (u_{X/Y', Q'} - 1). \end{equation} % Assume now that $Q \in B_{Y'/Y}$. Then there exists a unique point $Q' \in Y'(k)$ - in the preimage of $Q$ through $Y' \to Y$. Moreover, $m_{X/Y, Q} = n$, $m_{X/Y', Q'} = n-1$. + in the preimage of $Q$ through ${\color{red} \phi:}Y' \to Y$. Moreover, $m_{X/Y, Q} = n$, $m_{X/Y', Q'} = n-1$. Recall also that by {\color{red} \cite[Example p.76]{Serre1979} @@ -491,7 +491,7 @@ shows that $m_{\sigma - 1}$ is well-defined and injective. {\color{red} \[ \xymatrix{ - & X \ar[rd] \ar[ld] \ar[dd]^{\pi}& \\ + & X \ar[rd]^{\langle \sigma^{p^{n-1}} \rangle} \ar[ld]_{\langle \sigma^p \rangle =H'} \ar[dd]^{\pi}& \\ Y' \ar[rd]^{\phi} & & X'' \ar[ld]\\ & Y & } @@ -504,11 +504,11 @@ shows that $m_{\sigma - 1}$ is well-defined and injective. \mc M \cong \mc J_{p^{n-1}}^{2 p \cdot (g_Y - 1)} \oplus k^{\oplus 2}. \] % - Therefore $\dim_k \mc T^2 \mc M = \ldots = \dim_k \mc T^{p^{n-1}} \mc M = 2 p (g_Y - 1)$, + Therefore $\dim_k \mc T^2 \mc M = \cdots = \dim_k \mc T^{p^{n-1}} \mc M = 2 p (g_Y - 1)$, which by Lemma~\ref{lem:lemma_mcT_and_T} implies that % \[ - \dim_k T^p \mc M = \ldots = \dim_k T^{p^n} \mc M = 2(g_Y - 1) = \dim_k T^p \mc M_0. + \dim_k T^p \mc M = \cdots = \dim_k T^{p^n} \mc M = 2(g_Y - 1) = \dim_k T^p \mc M_0. \] % Thus, for $i = 2, \ldots, p$: @@ -547,7 +547,7 @@ shows that $m_{\sigma - 1}$ is well-defined and injective. &= p \cdot \left( 2(g_Y - 1) + 2 + 2(\# B - 1) + \sum_{Q' \in Y(k)} (u_{X/Y, Q'} - 1) \right). \end{align*} % - In particular, $\dim_k \mc T^1 \mc M = \ldots = \dim_k \mc T^{p^{n-1} - p^{n-2}} \mc M$. + In particular, $\dim_k \mc T^1 \mc M = \cdots = \dim_k \mc T^{p^{n-1} - p^{n-2}} \mc M$. Thus by Lemma~\ref{lem:lemma_mcT_and_T} for any $1 \le i \le p^n - p^{n-1}$: % \begin{align*} @@ -560,7 +560,7 @@ shows that $m_{\sigma - 1}$ is well-defined and injective. in $\FF_p[x]$ we have the identity: % \[ - 1 + x + \ldots + x^{p-1} = (x - 1)^{p-1}. + 1 + x + \cdots + x^{p-1} = (x - 1)^{p-1}. \] % Therefore in the group ring $k[H]$ we have: @@ -647,30 +647,30 @@ Let $X$ be a curve with an action of $G$ and write $Y := X/H$. For any $k[C]$-mo Note that % \[ - N \cong M^{\oplus 2} \oplus M^{\chi} \oplus M^{\chi^2} \oplus \ldots \oplus M^{\chi^{p-2}}. + N \cong M^{\oplus 2} \oplus M^{\chi} \oplus M^{\chi^2} \oplus \cdots \oplus M^{\chi^{p-2}}. \] % By tensoring this isomorphism by $\chi^i$ we obtain: % \begin{align*} - N^{\chi^i} \cong (M^{\chi^i})^{\oplus 2} \oplus M^{\chi^{i+1}} \oplus M^{\chi^{i+2}} \oplus \ldots \oplus M^{\chi^{i + p-2}} + N^{\chi^i} \cong (M^{\chi^i})^{\oplus 2} \oplus M^{\chi^{i+1}} \oplus M^{\chi^{i+2}} \oplus \cdots \oplus M^{\chi^{i + p-2}} \cong (M^{\chi^i})^{\oplus 2} \oplus \bigoplus_{\substack{j = 0\\j \neq i}}^{p-2} M^{\chi^j} \end{align*} % for $i = 0, \ldots, p-2$. Therefore: % \begin{equation} \label{eqn:M+N=N} - M^{\oplus p} \oplus N^{\chi} \oplus N^{\chi^2} \oplus \ldots \oplus N^{\chi^{p-2}} + M^{\oplus p} \oplus N^{\chi} \oplus N^{\chi^2} \oplus \cdots \oplus N^{\chi^{p-2}} \cong N^{\oplus (p-1)}. \end{equation} % Indeed, for the proof of~\eqref{eqn:M+N=N} note that % \begin{align*} - M^{\oplus p} &\oplus N^{\chi} \oplus N^{\chi^2} \oplus \ldots \oplus N^{\chi^{p-2}} + M^{\oplus p} &\oplus N^{\chi} \oplus N^{\chi^2} \oplus \cdots \oplus N^{\chi^{p-2}} \cong M^{\oplus p} \oplus \bigoplus_{i = 1}^{p-2} \left((M^{\chi^i})^{\oplus 2} \oplus \bigoplus_{\substack{j = 0\\j \neq i}}^{p-2} M^{\chi^j} \right)\\ - &\cong \left( M^{\oplus 2} \oplus M^{\chi} \oplus M^{\chi^2} \oplus \ldots \oplus M^{\chi^{p-2}} \right)^{\oplus (p-1)} + &\cong \left( M^{\oplus 2} \oplus M^{\chi} \oplus M^{\chi^2} \oplus \cdots \oplus M^{\chi^{p-2}} \right)^{\oplus (p-1)} \cong N^{\oplus (p-1)}. \end{align*} % @@ -691,13 +691,13 @@ Let $X$ be a curve with an action of $G$ and write $Y := X/H$. For any $k[C]$-mo % \[ (\sigma - 1) \cdot \rho = \rho \cdot (\sigma^{\chi(\rho)^{-1}} - 1) - = \rho \cdot (\sigma - 1) \cdot (1 + \sigma + \sigma^2 + \ldots + \sigma^{\chi(\rho)^{-1} - 1}) + = \rho \cdot (\sigma - 1) \cdot (1 + \sigma + \sigma^2 + \cdots + \sigma^{\chi(\rho)^{-1} - 1}) \] % Note that $\sigma$ acts trivially on $T^i M$, so that for any $\ol x \in T^i M$: % \[ - (1 + \sigma + \sigma^2 + \ldots + \sigma^{\chi(\rho)^{-1} - 1}) \cdot \ol x = \chi(\rho)^{-1} \cdot \ol x. + (1 + \sigma + \sigma^2 + \cdots + \sigma^{\chi(\rho)^{-1} - 1}) \cdot \ol x = \chi(\rho)^{-1} \cdot \ol x. \] % This easily shows that @@ -735,8 +735,8 @@ Let $X$ be a curve with an action of $G$ and write $Y := X/H$. For any $k[C]$-mo Thus, since the category of $k[C]$-modules is semisimple, for $i \le p^n - p^{n-1}$: % \begin{align*} - \mc T^i \mc M &\cong T^{pi - p + 1} \mc M \oplus \ldots \oplus T^{pi} \mc M\\ - &\cong T^1 \mc M \oplus (T^1 \mc M)^{\chi^{-1}} \oplus \ldots \oplus + \mc T^i \mc M &\cong T^{pi - p + 1} \mc M \oplus \cdots \oplus T^{pi} \mc M\\ + &\cong T^1 \mc M \oplus (T^1 \mc M)^{\chi^{-1}} \oplus \cdots \oplus (T^1 \mc M)^{\chi^{-p}}. \end{align*} % diff --git a/bibliografia.bib b/bibliografia.bib new file mode 100644 index 0000000..f73fcc5 --- /dev/null +++ b/bibliografia.bib @@ -0,0 +1,5327 @@ +@book {Alperin_local_rep, + AUTHOR = {Alperin, J. L.}, + TITLE = {Local representation theory}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {11}, + NOTE = {Modular representations as an introduction to the local + representation theory of finite groups}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1986}, + PAGES = {x+178}, + ISBN = {0-521-30660-4; 0-521-44926-X}, + MRCLASS = {20-02 (20C20)}, + MRNUMBER = {860771}, + MRREVIEWER = {Peter\ W.\ Donovan}, + DOI = {10.1017/CBO9780511623592}, + URL = {https://doi.org/10.1017/CBO9780511623592}, +} + +@book {Steinberg_Representation_book, + AUTHOR = {Steinberg, B.}, + TITLE = {Representation theory of finite groups}, + SERIES = {Universitext}, + NOTE = {An introductory approach}, + PUBLISHER = {Springer, New York}, + YEAR = {2012}, + PAGES = {xiv+157}, + ISBN = {978-1-4614-0775-1}, + MRCLASS = {20C15 (20-01)}, + MRNUMBER = {2867444}, + MRREVIEWER = {Jamshid\ Moori}, + DOI = {10.1007/978-1-4614-0776-8}, + URL = {https://doi.org/10.1007/978-1-4614-0776-8}, +} + +@book {Curtis_Reiner_Methods_II, + AUTHOR = {Curtis, C. W. and Reiner, I.}, + TITLE = {Methods of representation theory. {V}ol. {II}}, + SERIES = {Pure and Applied Mathematics (New York)}, + NOTE = {With applications to finite groups and orders, + A Wiley-Interscience Publication}, + PUBLISHER = {John Wiley \& Sons, Inc., New York}, + YEAR = {1987}, + PAGES = {xviii+951}, + ISBN = {0-471-88871-0}, + MRCLASS = {20-02 (11Exx 18F25 19A31 19B28 19C99 20Cxx)}, + MRNUMBER = {892316}, + MRREVIEWER = {J.\ L.\ Alperin}, +} + +@misc{garnek_indecomposables, + title={Indecomposable direct summands of cohomologies of curves}, + author={Garnek, J.}, + year={2024}, + eprint={2410.03319}, + archivePrefix={arXiv}, + primaryClass={math.AG}, + url={https://arxiv.org/abs/2410.03319}, + note={arXiv 2410.03319} +} + +@article{laurent_kock_drinfeld, + author = {Laurent, L. and K{\"{o}}ck, B.}, + title = {The canonical representation of the Drinfeld curve}, + journal = {Mathematische Nachrichten}, + volume = {online first}, + number = {}, + pages = {}, + year = {2024}, + doi = {https://doi.org/10.1002/mana.202200402}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.202200402}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.202200402}, + abstract = {Abstract If C\$C\$ is a smooth projective curve over an algebraically closed field F\$\mathbb {F}\$ and G\$G\$ is a group of automorphisms of C\$C\$, the canonical representation of C\$C\$ is given by the induced F\$\mathbb {F}\$-linear action of G\$G\$ on the vector space H0C,ΩC\$H^0\left(C,\Omega \_C\right)\$ of holomorphic differentials on C\$C\$. Computing it is still an open problem in general when the cover C→C/G\$C \rightarrow C/G\$ is wildly ramified. In this paper, we fix a prime power q\$q\$, we consider the Drinfeld curve, that is, the curve C\$C\$ given by the equation XYq−XqY−Zq+1=0\${XY^q-X^qY-Z^{q+1}=0}\$ over F=Fq¯\$\mathbb {F}=\hspace{0.83328pt}\overline{\hspace{-0.83328pt}\mathbb {F}\_q\hspace{-0.83328pt}}\hspace{0.83328pt}\$ together with its standard action by G=SL2Fq\${G=SL\_2\left(\mathbb {F}\_q\right)}\$, and decompose H0C,ΩC\$H^0\left(C,\Omega \_C\right)\$ as a direct sum of indecomposable representations of G\$G\$, thus solving the aforementioned problem in this case.} +} + +@book {Benson_reps_and_vbs, + AUTHOR = {Benson, D. J.}, + TITLE = {Representations of elementary abelian {$p$}-groups and vector + bundles}, + SERIES = {Cambridge Tracts in Mathematics}, + VOLUME = {208}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2017}, + PAGES = {xvii+328}, + ISBN = {978-1-107-17417-7}, + MRCLASS = {20C20 (14J60 14L30)}, + MRNUMBER = {3585474}, + MRREVIEWER = {Alan\ Koch}, + DOI = {10.1017/9781316795699}, + URL = {https://doi.org/10.1017/9781316795699}, +} + +@article {Wheeler, + AUTHOR = {Wheeler, W. W.}, + TITLE = {Generic module theory}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {185}, + YEAR = {1996}, + NUMBER = {1}, + PAGES = {205--228}, + ISSN = {0021-8693,1090-266X}, + MRCLASS = {20C05}, + MRNUMBER = {1409984}, + MRREVIEWER = {M.\ E.\ Harris}, + DOI = {10.1006/jabr.1996.0322}, + URL = {https://doi.org/10.1006/jabr.1996.0322}, +} + +@article {FPS_generic_and_maximal, + AUTHOR = {Friedlander, E. M. and Pevtsova, J. and Suslin, A.}, + TITLE = {Generic and maximal {J}ordan types}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {168}, + YEAR = {2007}, + NUMBER = {3}, + PAGES = {485--522}, + ISSN = {0020-9910,1432-1297}, + MRCLASS = {20G10 (20G15)}, + MRNUMBER = {2299560}, + MRREVIEWER = {George\ J.\ McNinch}, + DOI = {10.1007/s00222-007-0037-2}, + URL = {https://doi.org/10.1007/s00222-007-0037-2}, +} + +@article {Prest, + AUTHOR = {Prest, M.}, + TITLE = {Wild representation type and undecidability}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {19}, + YEAR = {1991}, + NUMBER = {3}, + PAGES = {919--929}, + ISSN = {0092-7872,1532-4125}, + MRCLASS = {16G60 (03C60 03D35)}, + MRNUMBER = {1102994}, + MRREVIEWER = {Sheila\ Brenner}, + DOI = {10.1080/00927879108824178}, + URL = {https://doi.org/10.1080/00927879108824178}, +} + +@article {Higman, + AUTHOR = {Higman, D. G.}, + TITLE = {Indecomposable representations at characteristic {$p$}}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {21}, + YEAR = {1954}, + PAGES = {377--381}, + ISSN = {0012-7094,1547-7398}, + MRCLASS = {20.0X}, + MRNUMBER = {67896}, + MRREVIEWER = {B.\ Eckmann}, + URL = {http://projecteuclid.org/euclid.dmj/1077465741}, +} + +@article {Tanimoto_modular_reps, + AUTHOR = {Tanimoto, R.}, + TITLE = {A note on modular representations of elementary abelian + {$p$}-groups}, + JOURNAL = {Saitama Math. J.}, + FJOURNAL = {Saitama Mathematical Journal}, + VOLUME = {32}, + YEAR = {2019}, + PAGES = {19--34}, + ISSN = {0289-0739}, + MRCLASS = {20C20}, + MRNUMBER = {4369885}, +} + +@incollection {Benson_survey, + AUTHOR = {Benson, D. J.}, + TITLE = {A survey of modules of constant {J}ordan type and vector + bundles on projective space}, + BOOKTITLE = {Advances in representation theory of algebras}, + SERIES = {EMS Ser. Congr. Rep.}, + PAGES = {39--63}, + PUBLISHER = {Eur. Math. Soc., Z\"urich}, + YEAR = {2013}, + ISBN = {978-3-03719-125-5}, + MRCLASS = {20C20 (16G60 16S34 17C99)}, + MRNUMBER = {3220533}, + MRREVIEWER = {Yang-Hui\ He}, +} + +@article {CFP_constant_Jordan, + AUTHOR = {Carlson, J. F. and Friedlander, E. M. and Pevtsova, J.}, + TITLE = {Modules of constant {J}ordan type}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {614}, + YEAR = {2008}, + PAGES = {191--234}, + ISSN = {0075-4102,1435-5345}, + MRCLASS = {20G05 (14L15 16G70)}, + MRNUMBER = {2376286}, + MRREVIEWER = {Alan\ Koch}, + DOI = {10.1515/CRELLE.2008.006}, + URL = {https://doi.org/10.1515/CRELLE.2008.006}, +} + + +@article {Heller_Reiner_Reps_in_integers_I, + AUTHOR = {Heller, A. and Reiner, I.}, + TITLE = {Representations of cyclic groups in rings of integers. {I}}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {76}, + YEAR = {1962}, + PAGES = {73--92}, + ISSN = {0003-486X}, + MRCLASS = {20.80}, + MRNUMBER = {140575}, + MRREVIEWER = {Rimhak\ Ree}, + DOI = {10.2307/1970266}, + URL = {https://doi.org/10.2307/1970266}, +} + +@article {Borevic_Faddeev, + AUTHOR = {{Borevi\v{c}}, Z. I. and Faddeev, D. K.}, + TITLE = {Theory of homology in groups. {II}. {P}rojective resolutions + of finite groups}, + JOURNAL = {Vestnik Leningrad. Univ.}, + FJOURNAL = {Vestnik Leningrad. Univ.}, + VOLUME = {14}, + YEAR = {1959}, + NUMBER = {7}, + PAGES = {72--87}, + MRCLASS = {18.00}, + MRNUMBER = {106234}, + MRREVIEWER = {W.\ T.\ van Est}, +} + +@article {Lucas_theorem, + AUTHOR = {Lucas, E.}, + TITLE = {Sur les congruences des nombres eul\'eriens et les + coefficients diff\'erentiels des functions trigonom\'etriques + suivant un module premier}, + JOURNAL = {Bull. Soc. Math. France}, + FJOURNAL = {Bulletin de la Soci\'et\'e{} Math\'ematique de France}, + VOLUME = {6}, + YEAR = {1878}, + PAGES = {49--54}, + ISSN = {0037-9484}, + MRCLASS = {99-04}, + MRNUMBER = {1503769}, + URL = {http://www.numdam.org/item?id=BSMF_1878__6__49_1}, +} + +@article {Harbater_Stevenson_patching_thickening, + AUTHOR = {Harbater, D. and Stevenson, K. F.}, + TITLE = {Patching and thickening problems}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {212}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {272--304}, + ISSN = {0021-8693,1090-266X}, + MRCLASS = {14B10 (12F12 14B12 14H30)}, + MRNUMBER = {1670658}, + MRREVIEWER = {Hiroaki\ Nakamura}, + DOI = {10.1006/jabr.1998.7574}, + URL = {https://doi.org/10.1006/jabr.1998.7574}, +} + +@incollection {Harbater_patching, + AUTHOR = {Harbater, D.}, + TITLE = {Patching and {G}alois theory}, + BOOKTITLE = {Galois groups and fundamental groups}, + SERIES = {Math. Sci. Res. Inst. Publ.}, + VOLUME = {41}, + PAGES = {313--424}, + PUBLISHER = {Cambridge Univ. Press, Cambridge}, + YEAR = {2003}, + ISBN = {0-521-80831-6}, + MRCLASS = {14H30 (12F12 14G22)}, + MRNUMBER = {2012220}, + MRREVIEWER = {Robert\ M.\ Guralnick}, +} + +@article {Das_Kumar_inertia_alternating, + AUTHOR = {Das, S. and Kumar, M.}, + TITLE = {On the inertia conjecture for alternating group covers}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {224}, + YEAR = {2020}, + NUMBER = {9}, + PAGES = {106363, 14}, + ISSN = {0022-4049,1873-1376}, + MRCLASS = {11S15 (13B05 14G17 14H30)}, + MRNUMBER = {4083789}, + MRREVIEWER = {Alan\ Koch}, + DOI = {10.1016/j.jpaa.2020.106363}, + URL = {https://doi.org/10.1016/j.jpaa.2020.106363}, +} + +@article {Nicolas_Serre_formes_mod2, + AUTHOR = {Nicolas, J.-L. and Serre, J.-P.}, + TITLE = {Formes modulaires modulo 2: structure de l'alg\`ebre de + {H}ecke}, + JOURNAL = {C. R. Math. Acad. Sci. Paris}, + FJOURNAL = {Comptes Rendus Math\'{e}matique. Acad\'{e}mie des Sciences. + Paris}, + VOLUME = {350}, + YEAR = {2012}, + NUMBER = {9-10}, + PAGES = {449--454}, + ISSN = {1631-073X,1778-3569}, + MRCLASS = {11F25}, + MRNUMBER = {2929047}, + MRREVIEWER = {Dominic\ A.\ Lanphier}, + DOI = {10.1016/j.crma.2012.03.019}, + URL = {https://doi.org/10.1016/j.crma.2012.03.019}, +} + +@article {Medvedovsky_nilpotence_order, + AUTHOR = {Medvedovsky, A.}, + TITLE = {Nilpotence order growth of recursion operators in + characteristic {$p$}}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {12}, + YEAR = {2018}, + NUMBER = {3}, + PAGES = {693--722}, + ISSN = {1937-0652,1944-7833}, + MRCLASS = {11T55 (11B85 11F03 11F33)}, + MRNUMBER = {3815310}, + MRREVIEWER = {Dominic\ A.\ Lanphier}, + DOI = {10.2140/ant.2018.12.693}, + URL = {https://doi.org/10.2140/ant.2018.12.693}, +} + +@article {Bellaiche_self_correspondences, + AUTHOR = {Bella\"{\i}che, J.}, + TITLE = {On self-correspondences on curves}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {17}, + YEAR = {2023}, + NUMBER = {11}, + PAGES = {1867--1899}, + ISSN = {1937-0652,1944-7833}, + MRCLASS = {14A10 (14E05 14F20 37P99)}, + MRNUMBER = {4648850}, + DOI = {10.2140/ant.2023.17.1867}, + URL = {https://doi.org/10.2140/ant.2023.17.1867}, +} + +@article {FW_Kock_Galois_module_theory, + AUTHOR = {Fischbacher-Weitz, H. and K\"{o}ck, B.}, + TITLE = {Galois-module theory for wildly ramified covers of curves over + finite fields}, + NOTE = {With an appendix by B. K\"{o}ck and A. Marmora}, + JOURNAL = {Doc. Math.}, + FJOURNAL = {Documenta Mathematica}, + VOLUME = {24}, + YEAR = {2019}, + PAGES = {175--208}, + ISSN = {1431-0635,1431-0643}, + MRCLASS = {11R58 (14G10 14G15 14H30)}, + MRNUMBER = {3946710}, + MRREVIEWER = {Takehiro\ Hasegawa}, +} + +@article {Commelin_MT_for_products, + AUTHOR = {Commelin, J.}, + TITLE = {The {M}umford-{T}ate conjecture for products of abelian + varieties}, + JOURNAL = {Algebr. Geom.}, + FJOURNAL = {Algebraic Geometry}, + VOLUME = {6}, + YEAR = {2019}, + NUMBER = {6}, + PAGES = {650--677}, + ISSN = {2313-1691,2214-2584}, + MRCLASS = {14F20 (14K15)}, + MRNUMBER = {4009176}, + MRREVIEWER = {Alessandra\ Bertapelle}, + DOI = {10.14231/ag-2019-028}, + URL = {https://doi.org/10.14231/ag-2019-028}, +} + +@article {Ribet_Hodge_classes_certain, + AUTHOR = {Ribet, K. A.}, + TITLE = {Hodge classes on certain types of abelian varieties}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {105}, + YEAR = {1983}, + NUMBER = {2}, + PAGES = {523--538}, + ISSN = {0002-9327,1080-6377}, + MRCLASS = {14K22 (11G10 11G40 14C30)}, + MRNUMBER = {701568}, + MRREVIEWER = {Yu.\ G.\ Zarkhin}, + DOI = {10.2307/2374267}, + URL = {https://doi.org/10.2307/2374267}, +} + +@article {Farfan_torsion_type_iii, + AUTHOR = {Cantoral Farf\'{a}n, V.}, + TITLE = {Torsion for abelian varieties of type {III}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {198}, + YEAR = {2019}, + PAGES = {346--380}, + ISSN = {0022-314X,1096-1658}, + MRCLASS = {11G10 (11F80 14K15)}, + MRNUMBER = {3912942}, + MRREVIEWER = {Neil\ P.\ Dummigan}, + DOI = {10.1016/j.jnt.2018.10.017}, + URL = {https://doi.org/10.1016/j.jnt.2018.10.017}, +} + +@article {Chi_IV, + AUTHOR = {Chi, W. Ch.}, + TITLE = {On the {$l$}-adic representations attached to simple abelian + varieties of type {${\rm IV}$}}, + JOURNAL = {Bull. Austral. Math. Soc.}, + FJOURNAL = {Bulletin of the Australian Mathematical Society}, + VOLUME = {44}, + YEAR = {1991}, + NUMBER = {1}, + PAGES = {71--78}, + ISSN = {0004-9727}, + MRCLASS = {11G10 (11G15 14K05)}, + MRNUMBER = {1120395}, + MRREVIEWER = {Nigel\ Boston}, + DOI = {10.1017/S0004972700029476}, + URL = {https://doi.org/10.1017/S0004972700029476}, +} + +@article {Zarhin_endo_Jacobians_cyclic_covers, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {The endomorphism rings of {J}acobians of cyclic covers of the + projective line}, + JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, + FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical + Society}, + VOLUME = {136}, + YEAR = {2004}, + NUMBER = {2}, + PAGES = {257--267}, + ISSN = {0305-0041,1469-8064}, + MRCLASS = {11G10 (14H40)}, + MRNUMBER = {2040573}, + MRREVIEWER = {Ivica\ Gusi\'{c}}, + DOI = {10.1017/S0305004103007102}, + URL = {https://doi.org/10.1017/S0305004103007102}, +} + +@phdthesis{van_bommel_2014, + title={Almost all hyperelliptic Jacobians have a bad semi-abelian prime}, + author={van Bommel, R.}, + year={2014} +} + +@article {Legrand_twists_superelliptic, + AUTHOR = {Legrand, F.}, + TITLE = {Twists of superelliptic curves without rational points}, + JOURNAL = {Int. Math. Res. Not. IMRN}, + FJOURNAL = {International Mathematics Research Notices. IMRN}, + YEAR = {2018}, + NUMBER = {4}, + PAGES = {1153--1176}, + ISSN = {1073-7928,1687-0247}, + MRCLASS = {11G05 (14H50)}, + MRNUMBER = {3801458}, + MRREVIEWER = {Martin\ Epkenhans}, + DOI = {10.1093/imrn/rnw270}, + URL = {https://doi.org/10.1093/imrn/rnw270}, +} + +@article {Rasmussen_Tamagawa_cyclic_covers_ihara, + AUTHOR = {Rasmussen, Ch. and Tamagawa, A.}, + TITLE = {Cyclic covers and {I}hara's question}, + JOURNAL = {Res. Number Theory}, + FJOURNAL = {Research in Number Theory}, + VOLUME = {5}, + YEAR = {2019}, + NUMBER = {4}, + PAGES = {Paper No. 33, 23}, + ISSN = {2522-0160,2363-9555}, + MRCLASS = {14H40 (11F80 11G10 11G30)}, + MRNUMBER = {4018545}, + MRREVIEWER = {Benjamin\ Smith}, + DOI = {10.1007/s40993-019-0170-1}, + URL = {https://doi.org/10.1007/s40993-019-0170-1}, +} + +@article {Beneish_locally_soluble, + AUTHOR = {Beneish, L. and Keyes, Ch.}, + TITLE = {On the proportion of locally soluble superelliptic curves}, + JOURNAL = {Finite Fields Appl.}, + FJOURNAL = {Finite Fields and their Applications}, + VOLUME = {85}, + YEAR = {2023}, + PAGES = {Paper No. 102128, 85}, + ISSN = {1071-5797,1090-2465}, + MRCLASS = {11G30 (11G20)}, + MRNUMBER = {4513718}, + MRREVIEWER = {Yves\ Aubry}, + DOI = {10.1016/j.ffa.2022.102128}, + URL = {https://doi.org/10.1016/j.ffa.2022.102128}, +} + +@inproceedings {Sutherland_counting_superelliptic, + AUTHOR = {Sutherland, A. V.}, + TITLE = {Counting points on superelliptic curves in average polynomial + time}, + BOOKTITLE = {A{NTS} {XIV}---{P}roceedings of the {F}ourteenth {A}lgorithmic + {N}umber {T}heory {S}ymposium}, + SERIES = {Open Book Ser.}, + VOLUME = {4}, + PAGES = {403--422}, + PUBLISHER = {Math. Sci. Publ., Berkeley, CA}, + YEAR = {2020}, + ISBN = {978-1-935107-08-8; 978-1-935107-07-1}, + MRCLASS = {11G20 (11M38 11Y16 14G10)}, + MRNUMBER = {4235126}, + DOI = {10.2140/obs.2020.4.403}, + URL = {https://doi.org/10.2140/obs.2020.4.403}, +} + +@article {Zarhin_cyclic_covers, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {Cyclic covers of the projective line, their {J}acobians and + endomorphisms}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {544}, + YEAR = {2002}, + PAGES = {91--110}, + ISSN = {0075-4102,1435-5345}, + MRCLASS = {11G10 (14C30 14K15)}, + MRNUMBER = {1887891}, + MRREVIEWER = {Ivica\ Gusi\'{c}}, + DOI = {10.1515/crll.2002.030}, + URL = {https://doi.org/10.1515/crll.2002.030}, +} + +@misc{Farfan_Survey_HTMTC, + Author = {Cantoral Farf\'{a}n, V.}, + Title = {A survey around the {H}odge, {T}ate and {M}umford-{T}ate conjectures for abelian varieties}, + Year = {2016}, + Eprint = {arXiv:1602.08354}, + note = {arXiv:1602.08354}, +} + +@article {Ghidelli_Arbitrarily_long, + AUTHOR = {Ghidelli, L.}, + TITLE = {Arbitrarily long gaps between the values of positive-definite + cubic and biquadratic diagonal forms}, + JOURNAL = {J. Lond. Math. Soc. (2)}, + FJOURNAL = {Journal of the London Mathematical Society. Second Series}, + VOLUME = {102}, + YEAR = {2020}, + NUMBER = {1}, + PAGES = {43--68}, + ISSN = {0024-6107,1469-7750}, + MRCLASS = {11D85 (11B05 11P05 11R37 11R45)}, + MRNUMBER = {4143726}, + MRREVIEWER = {Timothy\ Lee\ Gillespie}, + DOI = {10.1112/jlms.12312}, + URL = {https://doi.org/10.1112/jlms.12312}, +} + +@article {Banaszak_Kaim_Garnek_Tate_module_type_IV, + AUTHOR = {Banaszak, G. and Kaim-Garnek, A.}, + TITLE = {The {T}ate module of a simple abelian variety of type {IV}}, + JOURNAL = {New York J. Math.}, + FJOURNAL = {New York Journal of Mathematics}, + VOLUME = {27}, + YEAR = {2021}, + PAGES = {1240--1257}, + ISSN = {1076-9803}, + MRCLASS = {11F80 (11G10 16K20)}, + MRNUMBER = {4302422}, + MRREVIEWER = {Adam\ Morgan}, + URL = {}, +} + +@incollection {Weigel_profinite_completion, + AUTHOR = {Weigel, T.}, + TITLE = {On the profinite completion of arithmetic groups of split + type}, + BOOKTITLE = {Lois d'alg\`ebres et vari\'{e}t\'{e}s alg\'{e}briques + ({C}olmar, 1991)}, + SERIES = {Travaux en Cours}, + VOLUME = {50}, + PAGES = {79--101}, + PUBLISHER = {Hermann, Paris}, + YEAR = {1996}, + ISBN = {2-7056-6280-4}, + MRCLASS = {14L15}, + MRNUMBER = {1600994}, + MRREVIEWER = {Antoine\ Chambert-Loir}, +} + +@article {Vasiu_surjectivity_criteria_i, + AUTHOR = {Vasiu, A.}, + TITLE = {Surjectivity criteria for {$p$}-adic representations. {I}}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {112}, + YEAR = {2003}, + NUMBER = {3}, + PAGES = {325--355}, + ISSN = {0025-2611,1432-1785}, + MRCLASS = {11S23 (14L17)}, + MRNUMBER = {2067042}, + MRREVIEWER = {Philippe\ Gille}, + DOI = {10.1007/s00229-003-0402-4}, + URL = {https://doi.org/10.1007/s00229-003-0402-4}, +} + +@book {Serre_course_arithmetic, + AUTHOR = {Serre, J.-P.}, + TITLE = {A course in arithmetic}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {No. 7}, + NOTE = {Translated from the French}, + PUBLISHER = {Springer-Verlag, New York-Heidelberg}, + YEAR = {1973}, + PAGES = {viii+115}, + MRCLASS = {12-02 (10CXX 10DXX)}, + MRNUMBER = {344216}, +} + +@misc{cantoral_lombardo_monodromy_QM_jacobians, + title={Monodromy groups of {J}acobians with definite quaternionic multiplication}, + author={Cantoral Farf\'{a}n, V. and Lombardo, D. and Voight, D.}, + year={2023}, + eprint={2303.00804}, + archivePrefix={arXiv}, + primaryClass={math.NT}, + notes={arXiv 2303.00804} +} + +@book {Lang_Algebra, + AUTHOR = {Lang, S.}, + TITLE = {Algebra}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {211}, + EDITION = {third}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2002}, + PAGES = {xvi+914}, + ISBN = {0-387-95385-X}, + MRCLASS = {00A05 (15-02)}, + MRNUMBER = {1878556}, + DOI = {10.1007/978-1-4613-0041-0}, + URL = {https://doi.org/10.1007/978-1-4613-0041-0}, +} + +@article {Fite_Gonzalez_Frobenius_distribution, + AUTHOR = {Fit\'{e}, F. and Gonz\'{a}lez, J. and Lario, + J.-C.}, + TITLE = {Frobenius distribution for quotients of {F}ermat curves of + prime exponent}, + JOURNAL = {Canad. J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {68}, + YEAR = {2016}, + NUMBER = {2}, + PAGES = {361--394}, + ISSN = {0008-414X,1496-4279}, + MRCLASS = {11D41 (11G10 11M50 14G10)}, + MRNUMBER = {3484371}, + MRREVIEWER = {A.\ Peth\H{o}}, + DOI = {10.4153/CJM-2015-028-x}, + URL = {https://doi.org/10.4153/CJM-2015-028-x}, +} + +@article {Hirabayashi_generalization_Maillet_Demyanenko, + AUTHOR = {Hirabayashi, M.}, + TITLE = {A generalization of {M}aillet and {D}emyanenko determinants}, + JOURNAL = {Acta Arith.}, + FJOURNAL = {Acta Arithmetica}, + VOLUME = {83}, + YEAR = {1998}, + NUMBER = {4}, + PAGES = {391--397}, + ISSN = {0065-1036,1730-6264}, + MRCLASS = {11R29 (11R20)}, + MRNUMBER = {1610490}, + MRREVIEWER = {Kurt\ Girstmair}, + DOI = {10.4064/aa-83-4-391-397}, + URL = {https://doi.org/10.4064/aa-83-4-391-397}, +} + +@article {Kucera_Formulae_relative_class_nb, + AUTHOR = {Ku\v{c}era, R.}, + TITLE = {Formulae for the relative class number of an imaginary abelian + field in the form of a product of determinants}, + JOURNAL = {Acta Math. Inform. Univ. Ostraviensis}, + FJOURNAL = {Acta Mathematica et Informatica Universitatis Ostraviensis}, + VOLUME = {10}, + YEAR = {2002}, + NUMBER = {1}, + PAGES = {79--83}, + ISSN = {1211-4774}, + MRCLASS = {11R29 (11R20)}, + MRNUMBER = {1943026}, + MRREVIEWER = {Charles\ J.\ Parry}, +} + +@book {Jacobson_lectures_abstract_algebra_II, + AUTHOR = {Jacobson, N.}, + TITLE = {Lectures in abstract algebra. {V}ol. {II}. {L}inear algebra}, + PUBLISHER = {D. Van Nostrand Co., Inc., Toronto-New York-London}, + YEAR = {1953}, + PAGES = {xii+280}, + MRCLASS = {09.1X}, + MRNUMBER = {53905}, + MRREVIEWER = {T.\ Nakayama}, +} + +@article {Vasiu_some_cases_MT, + AUTHOR = {Vasiu, A.}, + TITLE = {Some cases of the {M}umford-{T}ate conjecture and {S}himura + varieties}, + JOURNAL = {Indiana Univ. Math. J.}, + FJOURNAL = {Indiana University Mathematics Journal}, + VOLUME = {57}, + YEAR = {2008}, + NUMBER = {1}, + PAGES = {1--75}, + ISSN = {0022-2518,1943-5258}, + MRCLASS = {14K15 (11G18 14G35)}, + MRNUMBER = {2400251}, + MRREVIEWER = {Vasil\cprime \ \={I}.\ Andr\={\i}\u{\i}chuk}, + DOI = {10.1512/iumj.2008.57.3513}, + URL = {https://doi.org/10.1512/iumj.2008.57.3513}, +} + +@article {Dokchitser_Arithmetic_hyperelliptic, + AUTHOR = {Dokchitser, T. and Dokchitser, V. and Maistret, + C. and Morgan, A.}, + TITLE = {Arithmetic of hyperelliptic curves over local fields}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {385}, + YEAR = {2023}, + NUMBER = {3-4}, + PAGES = {1213--1322}, + ISSN = {0025-5831,1432-1807}, + MRCLASS = {11G20 (11G10 14D10 14F20 14H45)}, + MRNUMBER = {4566695}, + DOI = {10.1007/s00208-021-02319-y}, + URL = {https://doi.org/10.1007/s00208-021-02319-y}, +} + +@article {Landesman_hyperelliptic_maximal_Galois, + AUTHOR = {Landesman, A. and Swaminathan, A. A. and Tao, J. and + Xu, Y.}, + TITLE = {Hyperelliptic curves with maximal {G}alois action on the + torsion points of their {J}acobians}, + JOURNAL = {Indiana Univ. Math. J.}, + FJOURNAL = {Indiana University Mathematics Journal}, + VOLUME = {69}, + YEAR = {2020}, + NUMBER = {7}, + PAGES = {2461--2492}, + ISSN = {0022-2518,1943-5258}, + MRCLASS = {11G30 (11F80 11G10 11R32 14J40)}, + MRNUMBER = {4195609}, + MRREVIEWER = {Neil\ P.\ Dummigan}, + DOI = {10.1512/iumj.2020.69.8178}, + URL = {https://doi.org/10.1512/iumj.2020.69.8178}, +} + +@misc{milneANT, + author={Milne, J. S.}, + title={Algebraic Number Theory (v3.03)}, + year={2011}, + note={Available at www.jmilne.org/math/}, + pages={159+viii} +} + +@article{Rademacher_arithmetische, + title={Eine arithmetische {S}ummenformel}, + author={Rademacher, H.}, + journal={Monatshefte f{\"u}r Mathematik und Physik}, + volume={39}, + pages={221--228}, + year={1932}, + publisher={Springer} +} + +@book {Meara_quadratic_forms, + AUTHOR = {O'Meara, O. T.}, + TITLE = {Introduction to quadratic forms}, + SERIES = {Die Grundlehren der mathematischen Wissenschaften}, + VOLUME = {Band 117}, + PUBLISHER = {Academic Press, Inc., Publishers, New York; Springer-Verlag, + Berlin-G\"{o}ttingen-Heidelberg}, + YEAR = {1963}, + PAGES = {xi+342}, + MRCLASS = {10.16 (12.70)}, + MRNUMBER = {152507}, + MRREVIEWER = {K.\ Iwasawa}, +} + +@article {Hermitian_skew_hermitian_local_rings, + AUTHOR = {Cruickshank, J. and Quinlan, R. and Szechtman, + F.}, + TITLE = {Hermitian and skew hermitian forms over local rings}, + JOURNAL = {Linear Algebra Appl.}, + FJOURNAL = {Linear Algebra and its Applications}, + VOLUME = {551}, + YEAR = {2018}, + PAGES = {147--161}, + ISSN = {0024-3795,1873-1856}, + MRCLASS = {11E08 (11E39 15A63)}, + MRNUMBER = {3797940}, + MRREVIEWER = {Daniel\ B.\ Shapiro}, + DOI = {10.1016/j.laa.2018.04.009}, + URL = {https://doi.org/10.1016/j.laa.2018.04.009}, +} + +@article {Ribet_galois_action_real_multiplication, + AUTHOR = {Ribet, K. A.}, + TITLE = {Galois action on division points of {A}belian varieties with + real multiplications}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {98}, + YEAR = {1976}, + NUMBER = {3}, + PAGES = {751--804}, + ISSN = {0002-9327,1080-6377}, + MRCLASS = {14K15}, + MRNUMBER = {457455}, + MRREVIEWER = {Jacques\ V\'{e}lu}, + DOI = {10.2307/2373815}, + URL = {https://doi.org/10.2307/2373815}, +} + +@article {Tzermias_cyclotomic_torsion, + AUTHOR = {Tzermias, P.}, + TITLE = {Cyclotomic torsion on {F}ermat {J}acobians}, + JOURNAL = {Arch. Math. (Basel)}, + FJOURNAL = {Archiv der Mathematik}, + VOLUME = {95}, + YEAR = {2010}, + NUMBER = {1}, + PAGES = {19--24}, + ISSN = {0003-889X,1420-8938}, + MRCLASS = {11G30 (14G05)}, + MRNUMBER = {2671233}, + MRREVIEWER = {Pete\ L.\ Clark}, + DOI = {10.1007/s00013-010-0141-1}, + URL = {https://doi.org/10.1007/s00013-010-0141-1}, +} + +@article {Tzermias_Explicit_rational, + AUTHOR = {Tzermias, P.}, + TITLE = {Explicit rational functions on {F}ermat curves and a theorem + of {G}reenberg}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {122}, + YEAR = {2000}, + NUMBER = {3}, + PAGES = {337--345}, + ISSN = {0010-437X,1570-5846}, + MRCLASS = {11G30 (14G05)}, + MRNUMBER = {1781335}, + MRREVIEWER = {Dino\ J.\ Lorenzini}, + DOI = {10.1023/A:1002461930939}, + URL = {https://doi.org/10.1023/A:1002461930939}, +} + +@article {Garnek_maximally_disjoint, + AUTHOR = {Garnek, J.}, + TITLE = {Products of hyperelliptic {J}acobians with maximal {G}alois + image}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {152}, + YEAR = {2024}, + NUMBER = {4}, + PAGES = {1419--1435}, + ISSN = {0002-9939,1088-6826}, + MRCLASS = {11G10 (11F80 14H40)}, + MRNUMBER = {4709215}, + DOI = {10.1090/proc/16628}, + URL = {https://doi.org/10.1090/proc/16628}, +} + +@misc{fite_ordinary_primes, + title={Ordinary primes for some varieties with extra endomorphisms}, + author={Fit\'{e}, F.}, + year={2023}, + eprint={2005.10185}, + archivePrefix={arXiv}, + primaryClass={math.NT}, + notes={to appear in Publicacions Matem\'{a'}tiques} +} + +@misc{Garnek_exponential_torsion, + title={The "exponential" torsion of superelliptic {J}acobians}, + author={Garnek, J.}, + year={2024}, + eprint={2401.02377}, + archivePrefix={arXiv}, + primaryClass={math.AG}, + notes={arXiv 2401.02377} +} + +@misc{Garnek_p_gp_covers_ii, + title={$p$-group {G}alois covers of curves in characteristic $p$ {II}}, + author={Garnek, J.}, + year={2023}, + eprint={2308.13290}, + archivePrefix={arXiv}, + primaryClass={math.AG}, + notes={arxiv 2308.13290} +} + +@incollection {Coleman_stable_reductions, + AUTHOR = {Coleman, R.}, + TITLE = {Computing stable reductions}, + BOOKTITLE = {S\'{e}minaire de {T}h\'{e}orie des {N}ombres, {P}aris + 1985--86}, + SERIES = {Progr. Math.}, + VOLUME = {71}, + PAGES = {1--18}, + PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, + YEAR = {1987}, + ISBN = {0-8176-3369-3}, + MRCLASS = {11G20 (11D41 11G30 11L05 14H25)}, + MRNUMBER = {1017900}, + MRREVIEWER = {Christoph\ Klingenberg}, + DOI = {10.1007/978-1-4757-4267-1\_1}, + URL = {https://doi.org/10.1007/978-1-4757-4267-1_1}, +} + +@article {Bouw_Wewers_Computing_Lfcts_superelliptic, + AUTHOR = {Bouw, I. I. and Wewers, S.}, + TITLE = {Computing {$L$}-functions and semistable reduction of + superelliptic curves}, + JOURNAL = {Glasg. Math. J.}, + FJOURNAL = {Glasgow Mathematical Journal}, + VOLUME = {59}, + YEAR = {2017}, + NUMBER = {1}, + PAGES = {77--108}, + ISSN = {0017-0895,1469-509X}, + MRCLASS = {11G40 (11G20 14G10 14H50)}, + MRNUMBER = {3576328}, + MRREVIEWER = {Remke\ Kloosterman}, + DOI = {10.1017/S0017089516000057}, + URL = {https://doi.org/10.1017/S0017089516000057}, +} + +@misc{goodman_superelliptic, + title={Superelliptic curves with large {G}alois images}, + author={Goodman, P.}, + year={2020}, + eprint={2011.14461}, + archivePrefix={arXiv}, + primaryClass={math.NT} +} + +@misc{arul_torsion_fermat_quotients, + title={Torsion points on Fermat quotients of the form $y^n = x^d + 1$}, + author={Arul, V.}, + year={2020}, + eprint={1910.14251}, + archivePrefix={arXiv}, + primaryClass={math.AG} +} + +@article {Zarhin_non_isogenous_superelliptic, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {Non-isogenous superelliptic {J}acobians}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {253}, + YEAR = {2006}, + NUMBER = {3}, + PAGES = {537--554}, + ISSN = {0025-5874,1432-1823}, + MRCLASS = {14H40 (11G30 14K02)}, + MRNUMBER = {2221085}, + MRREVIEWER = {Bjorn\ Poonen}, + DOI = {10.1007/s00209-005-0921-7}, + URL = {https://doi.org/10.1007/s00209-005-0921-7}, +} + +@incollection {Zarhin_superelliptic_jacobians, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {Superelliptic {J}acobians}, + BOOKTITLE = {Diophantine geometry}, + SERIES = {CRM Series}, + VOLUME = {4}, + PAGES = {363--390}, + PUBLISHER = {Ed. Norm., Pisa}, + YEAR = {2007}, + ISBN = {978-88-7642-206-5; 88-7642-206-5}, + MRCLASS = {14K30 (11G35)}, + MRNUMBER = {2349666}, +} + +@article {Zarhin_endomorphisms_superelliptic, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {Endomorphisms of superelliptic {J}acobians}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {261}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {691--707}, + ISSN = {0025-5874,1432-1823}, + MRCLASS = {14H40 (11G10 11G30 14K05)}, + MRNUMBER = {2471095}, + DOI = {10.1007/s00209-008-0342-5}, + URL = {https://doi.org/10.1007/s00209-008-0342-5}, +} + +@article {Xue_Zarhin_Hodge_groups, + AUTHOR = {Xue, J. and Zarhin, Y. G.}, + TITLE = {Hodge groups of certain superelliptic {J}acobians}, + JOURNAL = {Math. Res. Lett.}, + FJOURNAL = {Mathematical Research Letters}, + VOLUME = {17}, + YEAR = {2010}, + NUMBER = {2}, + PAGES = {371--388}, + ISSN = {1073-2780}, + MRCLASS = {14H40 (14K05)}, + MRNUMBER = {2644383}, + MRREVIEWER = {Cristiana\ Bertolin}, + DOI = {10.4310/MRL.2010.v17.n2.a15}, + URL = {https://doi.org/10.4310/MRL.2010.v17.n2.a15}, +} + +@article {Xue_Hodge_groups_superelliptic, + AUTHOR = {Xue, J.}, + TITLE = {Hodge groups of certain superelliptic {J}acobians {II}}, + JOURNAL = {Math. Res. Lett.}, + FJOURNAL = {Mathematical Research Letters}, + VOLUME = {18}, + YEAR = {2011}, + NUMBER = {4}, + PAGES = {579--590}, + ISSN = {1073-2780}, + MRCLASS = {14H40}, + MRNUMBER = {2831828}, + MRREVIEWER = {Samuel\ Dalalyan}, + DOI = {10.4310/MRL.2011.v18.n4.a1}, + URL = {https://doi.org/10.4310/MRL.2011.v18.n4.a1}, +} + +@article {Xue_Endomorphisms_superelliptic, + AUTHOR = {Xue, J.}, + TITLE = {Endomorphism algebras of {J}acobians of certain superelliptic + curves}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {131}, + YEAR = {2011}, + NUMBER = {2}, + PAGES = {332--342}, + ISSN = {0022-314X,1096-1658}, + MRCLASS = {11G30 (11G10 11R18)}, + MRNUMBER = {2910215}, + MRREVIEWER = {Ivica\ Gusi\'{c}}, + DOI = {10.1016/j.jnt.2010.07.013}, + URL = {https://doi.org/10.1016/j.jnt.2010.07.013}, +} + +@book {Xue_Endomorphisms_Hodge_superelliptic, + AUTHOR = {Xue, J.}, + TITLE = {The endomorphism algebras and {H}odge groups of certain + superelliptic {J}acobians}, + NOTE = {Thesis (Ph.D.)--The Pennsylvania State University}, + PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, + YEAR = {2010}, + PAGES = {77}, + ISBN = {978-1124-36143-7}, + MRCLASS = {99-05}, + MRNUMBER = {2813970}, + URL = + {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3436210}, +} + +@article {Xue_Zarhin_centers_Hodge_superelliptic, + AUTHOR = {Xue, J. and Zarhin, Y. G.}, + TITLE = {Centers of {H}odge groups of superelliptic {J}acobians}, + JOURNAL = {Transform. Groups}, + FJOURNAL = {Transformation Groups}, + VOLUME = {15}, + YEAR = {2010}, + NUMBER = {2}, + PAGES = {449--482}, + ISSN = {1083-4362,1531-586X}, + MRCLASS = {14H40 (14H45 14K12)}, + MRNUMBER = {2657449}, + MRREVIEWER = {Samuel\ Dalalyan}, + DOI = {10.1007/s00031-010-9085-6}, + URL = {https://doi.org/10.1007/s00031-010-9085-6}, +} + +@article {Jedrzejak_torsion_superelliptic, + AUTHOR = {J\k{e}drzejak, T.}, + TITLE = {On the torsion of the {J}acobians of superelliptic curves + {$y^q=x^p+a$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {145}, + YEAR = {2014}, + PAGES = {402--425}, + ISSN = {0022-314X,1096-1658}, + MRCLASS = {11G05 (14G25)}, + MRNUMBER = {3253312}, + MRREVIEWER = {Ariyan\ Javanpeykar}, + DOI = {10.1016/j.jnt.2014.06.013}, + URL = {https://doi.org/10.1016/j.jnt.2014.06.013}, +} + +@incollection {Jedrzejak_note_on_torsion, + AUTHOR = {J\k{e}drzejak, T.}, + TITLE = {A note on the torsion of the {J}acobians of superelliptic + curves {$y^q=x^p+a$}}, + BOOKTITLE = {Algebra, logic and number theory}, + SERIES = {Banach Center Publ.}, + VOLUME = {108}, + PAGES = {143--149}, + PUBLISHER = {Polish Acad. Sci. Inst. Math., Warsaw}, + YEAR = {2016}, + ISBN = {978-83-86806-31-7}, + MRCLASS = {11G10 (11G20 11L05 11R45)}, + MRNUMBER = {3559260}, +} + +@incollection {Zarhin_Endomorphisms_reference_superelliptic, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {Endomorphism algebras of abelian varieties with special + reference to superelliptic {J}acobians}, + BOOKTITLE = {Geometry, algebra, number theory, and their information + technology applications}, + SERIES = {Springer Proc. Math. Stat.}, + VOLUME = {251}, + PAGES = {477--528}, + PUBLISHER = {Springer, Cham}, + YEAR = {2018}, + ISBN = {978-3-319-97379-1; 978-3-319-97378-4}, + MRCLASS = {14H40 (11G10 11G30 14K05)}, + MRNUMBER = {3880401}, + MRREVIEWER = {Pawe\l \ Bor\'{o}wka}, + DOI = {10.1007/978-3-319-97379-1\_22}, + URL = {https://doi.org/10.1007/978-3-319-97379-1_22}, +} + +@article {Arul_division, + AUTHOR = {Arul, V.}, + TITLE = {Division by {$1- \zeta$} on superelliptic curves and + {J}acobians}, + JOURNAL = {Int. Math. Res. Not. IMRN}, + FJOURNAL = {International Mathematics Research Notices. IMRN}, + YEAR = {2021}, + NUMBER = {4}, + PAGES = {3143--3185}, + ISSN = {1073-7928,1687-0247}, + MRCLASS = {14H40 (11G10)}, + MRNUMBER = {4218349}, + MRREVIEWER = {Yves\ Aubry}, + DOI = {10.1093/imrn/rnaa075}, + URL = {https://doi.org/10.1093/imrn/rnaa075}, +} + +@incollection {Zarhin_Endomorphisms_ordinary_superelliptic, + AUTHOR = {Zarhin, Y. G.}, + TITLE = {Endomorphisms of ordinary superelliptic {J}acobians}, + BOOKTITLE = {Abelian varieties and number theory}, + SERIES = {Contemp. Math.}, + VOLUME = {767}, + PAGES = {51--69}, + PUBLISHER = {Amer. Math. Soc., [Providence], RI}, + YEAR = {[2021] \copyright 2021}, + ISBN = {978-1-4704-5207-0}, + MRCLASS = {14H40 (11G10 11G30 14K05)}, + MRNUMBER = {4252295}, + MRREVIEWER = {Jeroen\ Hanselman}, + DOI = {10.1090/conm/767/15397}, + URL = {https://doi.org/10.1090/conm/767/15397}, +} + +@article {Wawrow_torsion_superelliptic, + AUTHOR = {Wawr\'{o}w, W.}, + TITLE = {On torsion of superelliptic {J}acobians}, + JOURNAL = {J. Th\'{e}or. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'{e}orie des Nombres de Bordeaux}, + VOLUME = {33}, + YEAR = {2021}, + NUMBER = {1}, + PAGES = {223--235}, + ISSN = {1246-7405,2118-8572}, + MRCLASS = {14H40 (11G30 14G10 14H45)}, + MRNUMBER = {4312706}, + MRREVIEWER = {Zijian\ Zhou}, + URL = {http://jtnb.cedram.org/item?id=JTNB_2021__33_1_223_0}, +} + +@article {Pacetti_Villanueva_Galois_reps_superelliptic, + AUTHOR = {Pacetti, A. and Villanueva, A.}, + TITLE = {Galois representations of superelliptic curves}, + JOURNAL = {Glasg. Math. J.}, + FJOURNAL = {Glasgow Mathematical Journal}, + VOLUME = {65}, + YEAR = {2023}, + NUMBER = {2}, + PAGES = {356--382}, + ISSN = {0017-0895,1469-509X}, + MRCLASS = {11G20 (11F80)}, + MRNUMBER = {4625990}, + DOI = {10.1017/S0017089522000386}, + URL = {https://doi.org/10.1017/S0017089522000386}, +} + +@article {Garnek_p_gp_covers, + AUTHOR = {Garnek, J.}, + TITLE = {{$p$}-group {G}alois covers of curves in characteristic {$p$}}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {376}, + YEAR = {2023}, + NUMBER = {8}, + PAGES = {5857--5897}, + ISSN = {0002-9947,1088-6850}, + MRCLASS = {14F40 (14G17 14H30)}, + MRNUMBER = {4630761}, + DOI = {10.1090/tran/8932}, + URL = {https://doi.org/10.1090/tran/8932}, +} + +@InCollection{Glass_Pries_Klein_covers, + Author = {Glass, D. and Pries, R.}, + Title = {On the moduli space of {Klein} four covers of the projective line}, + BookTitle = {Computational aspects of algebraic curves. Papers from the conference, University of Idaho, Moscow, ID, USA, May 26--28, 2005}, + ISBN = {981-256-459-4}, + Pages = {58--70}, + Year = {2005}, + Publisher = {Hackensack, NJ: World Scientific}, + Language = {English}, + Keywords = {14H10,14H30}, + zbMATH = {5173409}, + Zbl = {1120.14017} +} + +@Article{Glass_Klein_covers, + Author = {Glass, D.}, + Title = {Klein-four covers of the projective line in characteristic two}, + FJournal = {Albanian Journal of Mathematics}, + Journal = {Albanian J. Math.}, + ISSN = {1930-1235}, + Volume = {1}, + Number = {1}, + Pages = {3--11}, + Year = {2007}, + Language = {English}, + Keywords = {14H30,14H37,14H45}, + URL = {x.kerkoje.com/index.php/ajm/article/view/1/1}, + zbMATH = {5190916}, + Zbl = {1123.14017} +} + +@article {Wu_Scheidler_Ramification_groups_AS_extensions, + AUTHOR = {Wu, Q. and Scheidler, R.}, + TITLE = {The ramification groups and different of a compositum of + {A}rtin-{S}chreier extensions}, + JOURNAL = {Int. J. Number Theory}, + FJOURNAL = {International Journal of Number Theory}, + VOLUME = {6}, + YEAR = {2010}, + NUMBER = {7}, + PAGES = {1541--1564}, + ISSN = {1793-0421}, + MRCLASS = {11R58 (11R20)}, + MRNUMBER = {2740721}, + MRREVIEWER = {Nigel Byott}, + DOI = {10.1142/S1793042110003617}, + URL = {https://doi-1org-102eb17l619f1.han.amu.edu.pl/10.1142/S1793042110003617}, +} + +@article {Basev_reps_Z2_Z2, + AUTHOR = {Ba\v{s}ev, V. A.}, + TITLE = {Representations of the group {$Z_{2}\times Z_{2}$} in a + field of characteristic {$2$}}, + JOURNAL = {Dokl. Akad. Nauk SSSR}, + FJOURNAL = {Doklady Akademii Nauk SSSR}, + VOLUME = {141}, + YEAR = {1961}, + PAGES = {1015--1018}, + ISSN = {0002-3264}, + MRCLASS = {20.80}, + MRNUMBER = {0132097}, + MRREVIEWER = {R. Kochend\"{o}rffer}, +} + +@article {Katz_local_to_global, + AUTHOR = {Katz, N. M.}, + TITLE = {Local-to-global extensions of representations of fundamental + groups}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {36}, + YEAR = {1986}, + NUMBER = {4}, + PAGES = {69--106}, + ISSN = {0373-0956}, + MRCLASS = {14H30 (14B20 14E20)}, + MRNUMBER = {867916}, + MRREVIEWER = {Noriko Yui}, + URL = {http://www-1numdam-1org-102eb17fv60ca.han.amu.edu.pl/item?id=AIF_1986__36_4_69_0}, +} + +@article{kontogeorgis_terezakis_new_obstruction, + title={A new obstruction to the local lifting problem}, + author={Kontogeorgis, A. and Terezakis, A.}, + year={2023}, + journal={arXiv:2304.08377} +} + +@book {Conway_Curtis_ATLAS, + AUTHOR = {Conway, J. H. and Curtis, R. T. and Norton, S. P. and Parker, + R. A. and Wilson, R. A.}, + TITLE = {{$\Bbb{ATLAS}$} of finite groups}, + NOTE = {Maximal subgroups and ordinary characters for simple groups, + With computational assistance from J. G. Thackray}, + PUBLISHER = {Oxford University Press, Eynsham}, + YEAR = {1985}, + PAGES = {xxxiv+252}, + ISBN = {0-19-853199-0}, + MRCLASS = {20D05 (20-02)}, + MRNUMBER = {827219}, + MRREVIEWER = {R. L. Griess}, +} + +@article {Katz_Nilpotent_Connections, + AUTHOR = {Katz, N. M.}, + TITLE = {Nilpotent connections and the monodromy theorem: + {A}pplications of a result of {T}urrittin}, + JOURNAL = {Inst. Hautes \'{E}tudes Sci. Publ. Math.}, + FJOURNAL = {Institut des Hautes \'{E}tudes Scientifiques. Publications + Math\'{e}matiques}, + NUMBER = {39}, + YEAR = {1970}, + PAGES = {175--232}, + ISSN = {0073-8301}, + MRCLASS = {14A99 (32C15)}, + MRNUMBER = {291177}, + MRREVIEWER = {S. S. Shatz}, + URL = {http://www-1numdam-1org-102eb17fv08e2.han.amu.edu.pl/item?id=PMIHES_1970__39__175_0}, +} + +@article {Bleher_Camacho_Holomorphic_differentials, + AUTHOR = {Bleher, F. M. and Camacho, N.}, + TITLE = {Holomorphic differentials of {K}lein four covers}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {227}, + YEAR = {2023}, + NUMBER = {10}, + PAGES = {Paper No. 107384, 27}, + ISSN = {0022-4049,1873-1376}, + MRCLASS = {14G17 (11G20 14H05 20C20)}, + MRNUMBER = {4576883}, + DOI = {10.1016/j.jpaa.2023.107384}, + URL = {https://doi.org/10.1016/j.jpaa.2023.107384}, +} + +@article {Collins_Modular_analogues, + AUTHOR = {Collins, M. J.}, + TITLE = {Modular analogues of {J}ordan's theorem for finite linear + groups}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {624}, + YEAR = {2008}, + PAGES = {143--171}, + ISSN = {0075-4102}, + MRCLASS = {20H20}, + MRNUMBER = {2456628}, + MRREVIEWER = {Timothy C. Burness}, + DOI = {10.1515/CRELLE.2008.084}, + URL = {https://doi-1org-102eb17ax5485.han.amu.edu.pl/10.1515/CRELLE.2008.084}, +} + + +@article {Larsen_Pink_Finite_subgroups, + AUTHOR = {Larsen, M. J. and Pink, R.}, + TITLE = {Finite subgroups of algebraic groups}, + JOURNAL = {J. Amer. Math. Soc.}, + FJOURNAL = {Journal of the American Mathematical Society}, + VOLUME = {24}, + YEAR = {2011}, + NUMBER = {4}, + PAGES = {1105--1158}, + ISSN = {0894-0347}, + MRCLASS = {20H20 (20G20)}, + MRNUMBER = {2813339}, + MRREVIEWER = {Peter A. Brooksbank}, + DOI = {10.1090/S0894-0347-2011-00695-4}, + URL = {https://doi-1org-102eb17ax5485.han.amu.edu.pl/10.1090/S0894-0347-2011-00695-4}, +} + +@article {Lombardo_Non-isogenous, + AUTHOR = {Lombardo, D.}, + TITLE = {Non-isogenous abelian varieties sharing the same division + fields}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {376}, + YEAR = {2023}, + NUMBER = {4}, + PAGES = {2615--2640}, + ISSN = {0002-9947}, + MRCLASS = {14K22 (11F80 11G10 14K15)}, + MRNUMBER = {4557876}, + DOI = {10.1090/tran/8767}, + URL = {https://doi-1org-102eb17qt3817.han.amu.edu.pl/10.1090/tran/8767}, +} + +@article{Daniels_Lozano_Conicidences, + author = {Daniels, H. B. and Lozano-Robledo, \'A.}, + title = {Coincidences of division fields}, + journal = {Annales de l'Institut Fourier}, + publisher = {Association des Annales de l{\textquoteright}institut Fourier}, + year = {2022}, + doi = {10.5802/aif.3520}, + language = {en}, + note = {Online first}, +} + +@book {Childs_Concrete_Higher_algebra, + AUTHOR = {Childs, L. N.}, + TITLE = {A concrete introduction to higher algebra}, + SERIES = {Undergraduate Texts in Mathematics}, + EDITION = {Third}, + PUBLISHER = {Springer, New York}, + YEAR = {2009}, + PAGES = {xiv+603}, + ISBN = {978-0-387-74527-5}, + MRCLASS = {00A05 (08-01 12-01 13-01 16-01 20-01)}, + MRNUMBER = {2464583}, + MRREVIEWER = {Kenneth A. Brown}, + DOI = {10.1007/978-0-387-74725-5}, + URL = {https://doi-1org-102eb17qt2f92.han.amu.edu.pl/10.1007/978-0-387-74725-5}, +} + +@book {Handbook_elliptic_hyperelliptic, + TITLE = {Handbook of elliptic and hyperelliptic curve cryptography}, + SERIES = {Discrete Mathematics and its Applications (Boca Raton)}, + EDITOR = {Cohen, H. and Frey, G. and Avanzi, R. and Doche, + C. and Lange, T. and Nguyen, K. and Vercauteren, + F.}, + PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL}, + YEAR = {2006}, + PAGES = {xxxiv+808}, + ISBN = {978-1-58488-518-4; 1-58488-518-1}, + MRCLASS = {14G50 (11G05 11G07 11T71 94-00 94A60)}, + MRNUMBER = {2162716}, + MRREVIEWER = {Steven D. Galbraith}, +} + +@article {Formanek_Sibley_gp_det, + AUTHOR = {Formanek, E. and Sibley, D.}, + TITLE = {The group determinant determines the group}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {112}, + YEAR = {1991}, + NUMBER = {3}, + PAGES = {649--656}, + ISSN = {0002-9939}, + MRCLASS = {20C15 (15A15 20C20)}, + MRNUMBER = {1062831}, + MRREVIEWER = {Burkhard K\"{u}lshammer}, + DOI = {10.2307/2048685}, + URL = {https://doi-1org-102eb172q0072.han.amu.edu.pl/10.2307/2048685}, +} + +@article {Madden_Arithmetic_generalized, + AUTHOR = {Madden, D. J.}, + TITLE = {Arithmetic in generalized {A}rtin-{S}chreier extensions of + {$k(x)$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {10}, + YEAR = {1978}, + NUMBER = {3}, + PAGES = {303--323}, + ISSN = {0022-314X}, + MRCLASS = {12A90 (14H05)}, + MRNUMBER = {506641}, + MRREVIEWER = {M. Fried}, + DOI = {10.1016/0022-314X(78)90027-6}, + URL = {https://doi-1org-102eb1776017a.han.amu.edu.pl/10.1016/0022-314X(78)90027-6}, +} + +@book {MacLane_Categories_working, + AUTHOR = {Mac Lane, S.}, + TITLE = {Categories for the working mathematician}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {5}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1998}, + PAGES = {xii+314}, + ISBN = {0-387-98403-8}, + MRCLASS = {18-02}, + MRNUMBER = {1712872}, +} + +@incollection {Kato_Log_structures_of_F_I, + AUTHOR = {Kato, K.}, + TITLE = {Logarithmic structures of {F}ontaine-{I}llusie}, + BOOKTITLE = {Algebraic analysis, geometry, and number theory ({B}altimore, + {MD}, 1988)}, + PAGES = {191--224}, + PUBLISHER = {Johns Hopkins Univ. Press, Baltimore, MD}, + YEAR = {1989}, + MRCLASS = {14F30 (14G20)}, + MRNUMBER = {1463703}, + MRREVIEWER = {Adolfo Quir\'{o}s}, +} + +@article {Guralnick_Roths_theorems, + AUTHOR = {Guralnick, R. M.}, + TITLE = {Roth's theorems and decomposition of modules}, + JOURNAL = {Linear Algebra Appl.}, + FJOURNAL = {Linear Algebra and its Applications}, + VOLUME = {39}, + YEAR = {1981}, + PAGES = {155--165}, + ISSN = {0024-3795}, + MRCLASS = {15A24 (16A64)}, + MRNUMBER = {625247}, + MRREVIEWER = {William H. Gustafson}, + DOI = {10.1016/0024-3795(81)90300-1}, + URL = {https://doi-1org-102eb170n00c5.han.amu.edu.pl/10.1016/0024-3795(81)90300-1}, +} + +@article{Buhler_Exact_Categories, + title = {Exact categories}, + journal = {Expositiones Mathematicae}, + volume = {28}, + number = {1}, + pages = {1-69}, + year = {2010}, + issn = {0723-0869}, + doi = {https://doi.org/10.1016/j.exmath.2009.04.004}, + url = {https://www.sciencedirect.com/science/article/pii/S0723086909000395}, + author = {Bühler, T.}, + keywords = {Exact categories, Diagram lemmas, Homological algebra, Derived functors, Derived categories, Embedding theorems}, +} + +@book {Ford_Sep_algebras, + AUTHOR = {Ford, T. J.}, + TITLE = {Separable algebras}, + SERIES = {Graduate Studies in Mathematics}, + VOLUME = {183}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2017}, + PAGES = {xxi+637}, + ISBN = {978-1-4704-3770-1}, + MRCLASS = {16-01 (13-01 13C20 16H05)}, + MRNUMBER = {3618889}, + MRREVIEWER = {Wolfgang Rump}, + DOI = {10.1090/gsm/183}, + URL = {https://doi-1org-102eb1784034d.han.amu.edu.pl/10.1090/gsm/183}, +} + +@article {Ellingsrud_Lonsted_Equivariant_Lefschetz, + AUTHOR = {Ellingsrud, G. and L{\o}nsted, K.}, + TITLE = {An equivariant {L}efschetz formula for finite reductive + groups}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {251}, + YEAR = {1980}, + NUMBER = {3}, + PAGES = {253--261}, + ISSN = {0025-5831}, + MRCLASS = {14L30 (55M99)}, + MRNUMBER = {589254}, + MRREVIEWER = {H. H. Andersen}, + DOI = {10.1007/BF01428945}, + URL = {https://doi-1org-102eb17cx014d.han.amu.edu.pl/10.1007/BF01428945}, +} + +@article {Ribet_Galois_action_on_division_points, + AUTHOR = {Ribet, K. A.}, + TITLE = {Galois action on division points of {A}belian varieties with + real multiplications}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {98}, + YEAR = {1976}, + NUMBER = {3}, + PAGES = {751--804}, + ISSN = {0002-9327}, + MRCLASS = {14K15}, + MRNUMBER = {457455}, + MRREVIEWER = {Jacques V\'{e}lu}, + DOI = {10.2307/2373815}, + URL = {https://doi-1org-102eb179r05d3.han.amu.edu.pl/10.2307/2373815}, +} + +@book {Lang_Trotter_Frobenius_distributions, + AUTHOR = {Lang, S. and Trotter, H.}, + TITLE = {Frobenius distributions in {${\rm GL}_{2}$}-extensions}, + SERIES = {Lecture Notes in Mathematics, Vol. 504}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1976}, + PAGES = {iii+274}, + MRCLASS = {12A50 (10K05)}, + MRNUMBER = {0568299}, + MRREVIEWER = {G. Frey}, +} + +@article {Serre_proprietes, + AUTHOR = {Serre, J.-P.}, + TITLE = {Propri\'{e}t\'{e}s galoisiennes des points d'ordre fini des courbes + elliptiques}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {15}, + YEAR = {1972}, + NUMBER = {4}, + PAGES = {259--331}, + ISSN = {0020-9910}, + MRCLASS = {14G25 (14K15)}, + MRNUMBER = {387283}, + MRREVIEWER = {J. W. S. Cassels}, + DOI = {10.1007/BF01405086}, + URL = {https://doi-1org-102eb17l403d2.han.amu.edu.pl/10.1007/BF01405086}, +} + +@book {SchurI, + AUTHOR = {Schur, I.}, + TITLE = {Gesammelte {A}bhandlungen. {B}and {I}}, + NOTE = {Herausgegeben von Alfred Brauer und Hans Rohrbach}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1973}, + PAGES = {xv+491 pp. (1 plate)}, + MRCLASS = {01A75}, + MRNUMBER = {0462891}, +} + +@article {Jones_Almost_all_ECs_are_Serre, + AUTHOR = {Jones, N.}, + TITLE = {Almost all elliptic curves are {S}erre curves}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {362}, + YEAR = {2010}, + NUMBER = {3}, + PAGES = {1547--1570}, + ISSN = {0002-9947}, + MRCLASS = {11G05 (11F80 11R45)}, + MRNUMBER = {2563740}, + MRREVIEWER = {Ravi K. Ramakrishna}, + DOI = {10.1090/S0002-9947-09-04804-1}, + URL = {https://doi-1org-102eb17p3016b.han.amu.edu.pl/10.1090/S0002-9947-09-04804-1}, +} + + +@book {OMeara_Symplectic_groups, + AUTHOR = {O'Meara, O. T.}, + TITLE = {Symplectic groups}, + SERIES = {Mathematical Surveys, No. 16}, + PUBLISHER = {American Mathematical Society, Providence, R.I.}, + YEAR = {1978}, + PAGES = {xi+122}, + ISBN = {0-8218-1516-4}, + MRCLASS = {20G05 (10C30 20E36 20F28)}, + MRNUMBER = {502254}, + MRREVIEWER = {E. A. Connors}, +} + +@article {Witt_Zyklische_Korper, + AUTHOR = {Witt, E.}, + TITLE = {Zyklische {K}\"{o}rper und {A}lgebren der {C}harakteristik {$p$} + vom {G}rad {$p^n$}. {S}truktur diskret bewerteter perfekter + {K}\"{o}rper mit vollkommenem {R}estklassenk\"{o}rper der + {C}harakteristik {$p$}}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {176}, + YEAR = {1937}, + PAGES = {126--140}, + ISSN = {0075-4102}, + MRCLASS = {DML}, + MRNUMBER = {1581526}, + DOI = {10.1515/crll.1937.176.126}, + URL = {https://doi-1org-102eb17fy0317.han.amu.edu.pl/10.1515/crll.1937.176.126}, +} + +@article {Saidi_Williams_Galois_covers_ppppp, + AUTHOR = {Sa\"{\i}di, M. and Williams, N.}, + TITLE = {Galois covers of type {$(p,\dots,p)$}, vanishing cycles + formula, and the existence of torsor structures}, + JOURNAL = {Osaka J. Math.}, + FJOURNAL = {Osaka Journal of Mathematics}, + VOLUME = {55}, + YEAR = {2018}, + NUMBER = {2}, + PAGES = {259--296}, + ISSN = {0030-6126}, + MRCLASS = {11G20 (14H30)}, + MRNUMBER = {3787745}, + MRREVIEWER = {Arman Shamsi Zargar}, + URL = {https://projecteuclid-1org-102eb17e60058.han.amu.edu.pl/euclid.ojm/1524038728}, +} + + +@article {Dobben_de_Br_Hodge_ring, + AUTHOR = {van Dobben de Bruyn, R.}, + TITLE = {The {H}odge ring of varieties in positive characteristic}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {15}, + YEAR = {2021}, + NUMBER = {3}, + PAGES = {729--745}, + ISSN = {1937-0652}, + MRCLASS = {14G17 (14A10 14F40)}, + MRNUMBER = {4261099}, + DOI = {10.2140/ant.2021.15.729}, + URL = {https://doi-1org-102eb17e60058.han.amu.edu.pl/10.2140/ant.2021.15.729}, +} + +@article {Tziolas_Quotients_alpha_p_mu_p, + AUTHOR = {Tziolas, N.}, + TITLE = {Quotients of schemes by {$\alpha_p$} or {$\mu_p$} actions in + characteristic {$p>0$}}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {152}, + YEAR = {2017}, + NUMBER = {1-2}, + PAGES = {247--279}, + ISSN = {0025-2611}, + MRCLASS = {14L30 (14D23 14J50 14L15)}, + MRNUMBER = {3595379}, + MRREVIEWER = {Yukihide Takayama}, + DOI = {10.1007/s00229-016-0854-y}, + URL = {https://doi-1org-102eb17lc001a.han.amu.edu.pl/10.1007/s00229-016-0854-y}, +} + +@article {Carlson_Friedlander_Suslin_Modules_for_Zp_Zp, + AUTHOR = {Carlson, J. F. and Friedlander, E. M. and Suslin, A.}, + TITLE = {Modules for {$\Bbb Z/p\times\Bbb Z/p$}}, + JOURNAL = {Comment. Math. Helv.}, + FJOURNAL = {Commentarii Mathematici Helvetici. A Journal of the Swiss + Mathematical Society}, + VOLUME = {86}, + YEAR = {2011}, + NUMBER = {3}, + PAGES = {609--657}, + ISSN = {0010-2571}, + MRCLASS = {20C20 (16G10 20G10)}, + MRNUMBER = {2803855}, + MRREVIEWER = {H\'{e}ctor A. Merklen}, + DOI = {10.4171/CMH/236}, + URL = {https://doi-1org-102eb17hj016a.han.amu.edu.pl/10.4171/CMH/236}, +} + + +@book {Hindry_Arithmetics, + AUTHOR = {Hindry, M.}, + TITLE = {Arithmetics}, + SERIES = {Universitext}, + NOTE = {Translated from the 2008 French original}, + PUBLISHER = {Springer, London}, + YEAR = {2011}, + PAGES = {xviii+321}, + ISBN = {978-1-4471-2130-5}, + MRCLASS = {11-01}, + MRNUMBER = {2816902}, + DOI = {10.1007/978-1-4471-2131-2}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.1007/978-1-4471-2131-2}, +} + +@article {Hindry_Silverman_canonical_height, + AUTHOR = {Hindry, M. and Silverman, J. H.}, + TITLE = {The canonical height and integral points on elliptic curves}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {93}, + YEAR = {1988}, + NUMBER = {2}, + PAGES = {419--450}, + ISSN = {0020-9910}, + MRCLASS = {11G05 (11D25 14G25)}, + MRNUMBER = {948108}, + MRREVIEWER = {Ernst-Ulrich Gekeler}, + DOI = {10.1007/BF01394340}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.1007/BF01394340}, +} + +@article {Hindry_conjecture_Lang, + AUTHOR = {Hindry, M.}, + TITLE = {Autour d'une conjecture de {S}erge {L}ang}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {94}, + YEAR = {1988}, + NUMBER = {3}, + PAGES = {575--603}, + ISSN = {0020-9910}, + MRCLASS = {11G10 (11J89 14K15)}, + MRNUMBER = {969244}, + MRREVIEWER = {Michel Laurent}, + DOI = {10.1007/BF01394276}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.1007/BF01394276}, +} + +@article {Hindry_David, + AUTHOR = {David, S. and Hindry, M.}, + TITLE = {Minoration de la hauteur de {N}\'{e}ron-{T}ate sur les vari\'{e}t\'{e}s + ab\'{e}liennes de type {C}. {M}}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {529}, + YEAR = {2000}, + PAGES = {1--74}, + ISSN = {0075-4102}, + MRCLASS = {11G50 (11G15 11J95 14G15 14K15)}, + MRNUMBER = {1799933}, + MRREVIEWER = {Carlo Gasbarri}, + DOI = {10.1515/crll.2000.096}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.1515/crll.2000.096}, +} + +@article {Hindry_Ratazzi_Points_de_torsion, + AUTHOR = {Hindry, Marc and Ratazzi, Nicolas}, + TITLE = {Points de torsion sur les vari\'{e}t\'{e}s ab\'{e}liennes de type {GS}p}, + JOURNAL = {J. Inst. Math. Jussieu}, + FJOURNAL = {Journal of the Institute of Mathematics of Jussieu. JIMJ. + Journal de l'Institut de Math\'{e}matiques de Jussieu}, + VOLUME = {11}, + YEAR = {2012}, + NUMBER = {1}, + PAGES = {27--65}, + ISSN = {1474-7480}, + MRCLASS = {11J95 (11G10 14K15)}, + MRNUMBER = {2862374}, + MRREVIEWER = {Konstantinos Draziotis}, + DOI = {10.1017/S147474801000023X}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.1017/S147474801000023X}, +} + +@article {Hindry_Ratazzi_torsion_pur, + AUTHOR = {Hindry, M. and Ratazzi, N.}, + TITLE = {Torsion pour les vari\'{e}t\'{e}s ab\'{e}liennes de type {I} et {II}}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {10}, + YEAR = {2016}, + NUMBER = {9}, + PAGES = {1845--1891}, + ISSN = {1937-0652}, + MRCLASS = {11G10 (11F80 14K15)}, + MRNUMBER = {3576113}, + MRREVIEWER = {Davide Lombardo}, + DOI = {10.2140/ant.2016.10.1845}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.2140/ant.2016.10.1845}, +} + +@article {Hindry_regulators, + AUTHOR = {Autissier, P. and Hindry, M. and Pazuki, F.}, + TITLE = {Regulators of elliptic curves}, + JOURNAL = {Int. Math. Res. Not. IMRN}, + FJOURNAL = {International Mathematics Research Notices. IMRN}, + YEAR = {2021}, + NUMBER = {7}, + PAGES = {4976--4993}, + ISSN = {1073-7928}, + MRCLASS = {11G50 (11G05 14H52)}, + MRNUMBER = {4241121}, + MRREVIEWER = {Dragos Ghioca}, + DOI = {10.1093/imrn/rny285}, + URL = {https://doi-1org-102eb171d0045.han.amu.edu.pl/10.1093/imrn/rny285}, +} + + +@article {Illusie_complexe_dR_Witt, + AUTHOR = {Illusie, L.}, + TITLE = {Complexe de de {R}ham-{W}itt et cohomologie cristalline}, + JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme + S\'{e}rie}, + VOLUME = {12}, + YEAR = {1979}, + NUMBER = {4}, + PAGES = {501--661}, + ISSN = {0012-9593}, + MRCLASS = {14F30}, + MRNUMBER = {565469}, + MRREVIEWER = {William E. Lang}, + URL = {http://www-1numdam-1org-102eb17ck02a0.han.amu.edu.pl/item?id=ASENS_1979_4_12_4_501_0}, +} + +@article {Lusztig_Coxeter_orbits, + AUTHOR = {Lusztig, G.}, + TITLE = {Coxeter orbits and eigenspaces of {F}robenius}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {38}, + YEAR = {1976/77}, + NUMBER = {2}, + PAGES = {101--159}, + ISSN = {0020-9910}, + MRCLASS = {20G05}, + MRNUMBER = {453885}, + MRREVIEWER = {David Kazhdan}, + DOI = {10.1007/BF01408569}, + URL = {https://doi-1org-102eb17k4003b.han.amu.edu.pl/10.1007/BF01408569}, +} + +@article {Gross_Rigid_local_systems_Gm, + AUTHOR = {Gross, B. H.}, + TITLE = {Rigid local systems on {$\Bbb G_m$} with finite monodromy}, + JOURNAL = {Adv. Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {224}, + YEAR = {2010}, + NUMBER = {6}, + PAGES = {2531--2543}, + ISSN = {0001-8708}, + MRCLASS = {20G40 (14G10 14L30 20G05)}, + MRNUMBER = {2652215}, + MRREVIEWER = {Jorge A. Vargas}, + DOI = {10.1016/j.aim.2010.02.008}, + URL = {https://doi-1org-102eb17k4003b.han.amu.edu.pl/10.1016/j.aim.2010.02.008}, +} + + +@article {Lusztig_Irreducible_representations_77, + AUTHOR = {Lusztig, G.}, + TITLE = {Irreducible representations of finite classical groups}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {43}, + YEAR = {1977}, + NUMBER = {2}, + PAGES = {125--175}, + ISSN = {0020-9910}, + MRCLASS = {20C15}, + MRNUMBER = {463275}, + MRREVIEWER = {James E. Humphreys}, + DOI = {10.1007/BF01390002}, + URL = {https://doi-1org-102eb17k4003b.han.amu.edu.pl/10.1007/BF01390002}, +} + +@article {Deligne_Lusztig_Representations_76, + AUTHOR = {Deligne, P. and Lusztig, G.}, + TITLE = {Representations of reductive groups over finite fields}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {103}, + YEAR = {1976}, + NUMBER = {1}, + PAGES = {103--161}, + ISSN = {0003-486X}, + MRCLASS = {20G05 (14M15)}, + MRNUMBER = {393266}, + MRREVIEWER = {S. I. Gel\cprime fand}, + DOI = {10.2307/1971021}, + URL = {https://doi-1org-102eb17k4003b.han.amu.edu.pl/10.2307/1971021}, +} + +@article {Liu_decomposition_suz, + AUTHOR = {Liu, L. Q.}, + TITLE = {The decomposition numbers of {${\rm Suz}(q)$}}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {172}, + YEAR = {1995}, + NUMBER = {1}, + PAGES = {1--31}, + ISSN = {0021-8693}, + MRCLASS = {20C34 (20C20)}, + MRNUMBER = {1320616}, + MRREVIEWER = {Leonard Chastkofsky}, + DOI = {10.1006/jabr.1995.1045}, + URL = {https://doi-1org-102eb17w20023.han.amu.edu.pl/10.1006/jabr.1995.1045}, +} + +@incollection {Malmskog_Pries_Weir_dR_Suzuki, + AUTHOR = {Malmskog, B. and Pries, R. and Weir, C.}, + TITLE = {The de {R}ham cohomology of the {S}uzuki curves}, + BOOKTITLE = {Arithmetic geometry: computation and applications}, + SERIES = {Contemp. Math.}, + VOLUME = {722}, + PAGES = {105--119}, + PUBLISHER = {Amer. Math. Soc., [Providence], RI}, + YEAR = {2019}, + MRCLASS = {11G10 (11G20 14F40 14H40 14L15 20C20 20C33)}, + MRNUMBER = {3896851}, + MRREVIEWER = {Yves Aubry}, + DOI = {10.1090/conm/722/14537}, + URL = {https://doi-1org-102eb17w20023.han.amu.edu.pl/10.1090/conm/722/14537}, +} + +@article {Dummigan_99, + AUTHOR = {Dummigan, N.}, + TITLE = {Complete {$p$}-descent for {J}acobians of {H}ermitian curves}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {119}, + YEAR = {1999}, + NUMBER = {2}, + PAGES = {111--132}, + ISSN = {0010-437X}, + MRCLASS = {11G20 (11G10 11G30 11G40 14F30)}, + MRNUMBER = {1723124}, + MRREVIEWER = {Massimo Bertolini}, + DOI = {10.1023/A:1001721808335}, + URL = {https://doi-1org-102eb17w20023.han.amu.edu.pl/10.1023/A:1001721808335}, +} + + +@article {Dummigan_95, + AUTHOR = {Dummigan, N.}, + TITLE = {The determinants of certain {M}ordell-{W}eil lattices}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {117}, + YEAR = {1995}, + NUMBER = {6}, + PAGES = {1409--1429}, + ISSN = {0002-9327}, + MRCLASS = {11G05 (11G40)}, + MRNUMBER = {1363073}, + MRREVIEWER = {John W. Jones}, + DOI = {10.2307/2375024}, + URL = {https://doi-1org-102eb17w20023.han.amu.edu.pl/10.2307/2375024}, +} + +@article {Haastert_Jantzen_Filtrations_crystalline, + AUTHOR = {Haastert, B. and Jantzen, J. C.}, + TITLE = {Filtrations of symmetric powers via crystalline cohomology}, + JOURNAL = {Geom. Dedicata}, + FJOURNAL = {Geometriae Dedicata}, + VOLUME = {37}, + YEAR = {1991}, + NUMBER = {1}, + PAGES = {45--63}, + ISSN = {0046-5755}, + MRCLASS = {14F30 (20G05)}, + MRNUMBER = {1094227}, + MRREVIEWER = {Jan Stienstra}, + DOI = {10.1007/BF00150404}, + URL = {https://doi-1org-102eb17w20023.han.amu.edu.pl/10.1007/BF00150404}, +} + +@article {Haastert_Jantzen_Filtrations, + AUTHOR = {Haastert, B. and Jantzen, J. C.}, + TITLE = {Filtrations of the discrete series of {${\rm SL}_2(q)$} via + crystalline cohomology}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {132}, + YEAR = {1990}, + NUMBER = {1}, + PAGES = {77--103}, + ISSN = {0021-8693}, + MRCLASS = {20G05 (14F30 20G40)}, + MRNUMBER = {1060833}, + MRREVIEWER = {Bhama Srinivasan}, + DOI = {10.1016/0021-8693(90)90253-K}, + URL = {https://doi-1org-102eb17w20023.han.amu.edu.pl/10.1016/0021-8693(90)90253-K}, +} + + +@article {Kontogeorgis_Tsouknidas_Cohomological_HKG, + AUTHOR = {Kontogeorgis, A. and Tsouknidas, I.}, + TITLE = {A cohomological treatise of {HKG}-covers with applications to + the {N}ottingham group}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {555}, + YEAR = {2020}, + PAGES = {325--345}, + ISSN = {0021-8693}, + MRCLASS = {14H30 (20E18 20J06)}, + MRNUMBER = {4081494}, + MRREVIEWER = {Jos\'{e} Javier Etayo}, + DOI = {10.1016/j.jalgebra.2020.02.037}, + URL = {https://doi-1org-102eb179p0007.han.amu.edu.pl/10.1016/j.jalgebra.2020.02.037}, +} + + +@article {Karanikolopoulos_Kontogeorgis_Autos, + AUTHOR = {Karanikolopoulos, S. and Kontogeorgis, A.}, + TITLE = {Automorphisms of curves and {W}eierstrass semigroups for + {H}arbater-{K}atz-{G}abber covers}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {371}, + YEAR = {2019}, + NUMBER = {9}, + PAGES = {6377--6402}, + ISSN = {0002-9947}, + MRCLASS = {14H37 (11G20 14H10 14H55 20M14)}, + MRNUMBER = {3937329}, + MRREVIEWER = {Mariana de Almeida Nery Coutinho}, + DOI = {10.1090/tran/7562}, + URL = {https://doi-1org-102eb179p0007.han.amu.edu.pl/10.1090/tran/7562}, +} + +@article {Obus_Wewers_Cyclic_extensions, + AUTHOR = {Obus, A. and Wewers, S.}, + TITLE = {Cyclic extensions and the local lifting problem}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {180}, + YEAR = {2014}, + NUMBER = {1}, + PAGES = {233--284}, + ISSN = {0003-486X}, + MRCLASS = {11G30 (11G20 11S15 14H25)}, + MRNUMBER = {3194815}, + MRREVIEWER = {Kevin P. Keating}, + DOI = {10.4007/annals.2014.180.1.5}, + URL = {https://doi-1org-102eb17iw0180.han.amu.edu.pl/10.4007/annals.2014.180.1.5}, +} + +@incollection {Obus_local_lifting_problem, + AUTHOR = {Obus, A.}, + TITLE = {The (local) lifting problem for curves}, + BOOKTITLE = {Galois-{T}eichm\"{u}ller theory and arithmetic geometry}, + SERIES = {Adv. Stud. Pure Math.}, + VOLUME = {63}, + PAGES = {359--412}, + PUBLISHER = {Math. Soc. Japan, Tokyo}, + YEAR = {2012}, + MRCLASS = {14H37 (11G20 14G17)}, + MRNUMBER = {3051249}, + MRREVIEWER = {Jeroen Sijsling}, + DOI = {10.2969/aspm/06310359}, + URL = {https://doi-1org-102eb17iw0180.han.amu.edu.pl/10.2969/aspm/06310359}, +} + +@article {Chinburg_Guralnick_Harbater_local_lifting_for_actions, + AUTHOR = {Chinburg, T. and Guralnick, R. and Harbater, D.}, + TITLE = {The local lifting problem for actions of finite groups on + curves}, + JOURNAL = {Ann. Sci. \'{E}c. Norm. Sup\'{e}r. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme + S\'{e}rie}, + VOLUME = {44}, + YEAR = {2011}, + NUMBER = {4}, + PAGES = {537--605}, + ISSN = {0012-9593}, + MRCLASS = {14H37 (12F10 14L30 20B25)}, + MRNUMBER = {2919977}, + MRREVIEWER = {Irene I. Bouw}, + DOI = {10.24033/asens.2150}, + URL = {https://doi-1org-102eb17iw0180.han.amu.edu.pl/10.24033/asens.2150}, +} + +@article {Chinburg_Guralnick_Harbater_Oort_groups_lifting, + AUTHOR = {Chinburg, T. and Guralnick, R. and Harbater, D.}, + TITLE = {Oort groups and lifting problems}, + JOURNAL = {Compos. Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {144}, + YEAR = {2008}, + NUMBER = {4}, + PAGES = {849--866}, + ISSN = {0010-437X}, + MRCLASS = {14L30 (14H37)}, + MRNUMBER = {2441248}, + MRREVIEWER = {Vasily A. Chernecky}, + DOI = {10.1112/S0010437X08003515}, + URL = {https://doi-1org-102eb17iw0180.han.amu.edu.pl/10.1112/S0010437X08003515}, +} + +@article {Kontogeorgis_Tsouknidas_generating_set_HKG, + AUTHOR = {Kontogeorgis, A. and Tsouknidas, I.}, + TITLE = {A generating set for the canonical ideal of {HKG}-curves}, + JOURNAL = {Res. Number Theory}, + FJOURNAL = {Research in Number Theory}, + VOLUME = {7}, + YEAR = {2021}, + NUMBER = {1}, + PAGES = {Paper No. 4, 16}, + ISSN = {2522-0160}, + MRCLASS = {14H55}, + MRNUMBER = {4194180}, + MRREVIEWER = {C\'{\i}cero Carvalho}, + DOI = {10.1007/s40993-020-00230-0}, + URL = {https://doi-1org-102eb17iw0180.han.amu.edu.pl/10.1007/s40993-020-00230-0}, +} + +@book {Arbarello_Griffiths_Geometry_curves_ii, + AUTHOR = {Arbarello, E. and Cornalba, M. and Griffiths, + P. A.}, + TITLE = {Geometry of algebraic curves. {V}olume {II}}, + SERIES = {Grundlehren der mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {268}, + NOTE = {With a contribution by Joseph Daniel Harris}, + PUBLISHER = {Springer, Heidelberg}, + YEAR = {2011}, + PAGES = {xxx+963}, + ISBN = {978-3-540-42688-2}, + MRCLASS = {14H10 (32G15)}, + MRNUMBER = {2807457}, + MRREVIEWER = {E. Looijenga}, + DOI = {10.1007/978-3-540-69392-5}, + URL = {https://doi.org/10.1007/978-3-540-69392-5}, +} + +@article {Booher_Pries_Realizing, + AUTHOR = {Booher, J. and Pries, R.}, + TITLE = {Realizing {A}rtin-{S}chreier covers of curves with minimal + {N}ewton polygons in positive characteristic}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {214}, + YEAR = {2020}, + PAGES = {240--250}, + ISSN = {0022-314X}, + MRCLASS = {11G20 (11M38 11T23 14G17 14H30 14H40)}, + MRNUMBER = {4105710}, + MRREVIEWER = {Antonio Rojas Le\'{o}n}, + DOI = {10.1016/j.jnt.2020.04.010}, + URL = {https://doi.org/10.1016/j.jnt.2020.04.010}, +} + +@article {Booher_Cais_a_numbers, + AUTHOR = {Booher, J. and Cais, B.}, + TITLE = {{$a$}-numbers of curves in {A}rtin-{S}chreier covers}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {14}, + YEAR = {2020}, + NUMBER = {3}, + PAGES = {587--641}, + ISSN = {1937-0652}, + MRCLASS = {14H30 (11G20 14G17 14H40)}, + MRNUMBER = {4113776}, + DOI = {10.2140/ant.2020.14.587}, + URL = {https://doi.org/10.2140/ant.2020.14.587}, +} + +@article {Borne_Cohomology_of_G_sheaves, + AUTHOR = {Borne, N.}, + TITLE = {Cohomology of {$G$}-sheaves in positive characteristic}, + JOURNAL = {Adv. Math.}, + FJOURNAL = {Advances in Mathematics}, + VOLUME = {201}, + YEAR = {2006}, + NUMBER = {2}, + PAGES = {454--515}, + ISSN = {0001-8708}, + MRCLASS = {14C35 (11R33 14L30 19D55)}, + MRNUMBER = {2211535}, + MRREVIEWER = {Claudio Pedrini}, + DOI = {10.1016/j.aim.2005.03.002}, + URL = {https://doi.org/10.1016/j.aim.2005.03.002}, +} + +@article {Kantor_Seress_Large_element_orders, + AUTHOR = {Kantor, W. M. and Seress, \'{A}.}, + TITLE = {Large element orders and the characteristic of {L}ie-type + simple groups}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {322}, + YEAR = {2009}, + NUMBER = {3}, + PAGES = {802--832}, + ISSN = {0021-8693}, + MRCLASS = {20D06}, + MRNUMBER = {2531224}, + MRREVIEWER = {Timothy C. Burness}, + DOI = {10.1016/j.jalgebra.2009.05.004}, + URL = {https://doi.org/10.1016/j.jalgebra.2009.05.004}, +} + +@article {Landesman_Lombardo_Surjectivity_Rational_Families, + AUTHOR = {Landesman, A. and Swaminathan, A. and Tao, J. and + Xu, Y.}, + TITLE = {Surjectivity of {G}alois representations in rational families + of abelian varieties}, + NOTE = {With an appendix by D. Lombardo}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {13}, + YEAR = {2019}, + NUMBER = {5}, + PAGES = {995--1038}, + ISSN = {1937-0652}, + MRCLASS = {11F80 (11G10 11G30 11N36 11R32 14K15)}, + MRNUMBER = {3981312}, + MRREVIEWER = {Jackson S. Morrow}, + DOI = {10.2140/ant.2019.13.995}, + URL = {https://doi.org/10.2140/ant.2019.13.995}, +} + +@article {Anni_Dokchitser_Constructing_hyperelliptic, + AUTHOR = {Anni, S. and Dokchitser, V.}, + TITLE = {Constructing hyperelliptic curves with surjective {G}alois + representations}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {373}, + YEAR = {2020}, + NUMBER = {2}, + PAGES = {1477--1500}, + ISSN = {0002-9947}, + MRCLASS = {11F80 (11G10 11G30 12F12)}, + MRNUMBER = {4068270}, + MRREVIEWER = {Valentijn Zo\"{e} Karemaker}, + DOI = {10.1090/tran/7995}, + URL = {https://doi.org/10.1090/tran/7995}, +} + +@Article{Yelton_Lifting_images, + author={Yelton, J.}, + title={Lifting images of standard representations of symmetric groups}, + fjournal={Manuscripta Mathematica}, + journal={Manuscripta Math.}, + year={2021}, + month={May}, + day={27}, + issn={1432-1785}, + doi={10.1007/s00229-021-01310-w}, + url={https://doi.org/10.1007/s00229-021-01310-w} +} + +@article {Landesman_Lifting_Symplectic, + AUTHOR = {Landesman, A. and Swaminathan, A. A. and Tao, J. and + Xu, Y.}, + TITLE = {Lifting subgroups of symplectic groups over + {$\Bbb{Z}/\ell\Bbb{Z}$}}, + JOURNAL = {Res. Number Theory}, + FJOURNAL = {Research in Number Theory}, + VOLUME = {3}, + YEAR = {2017}, + PAGES = {Paper No. 14, 12}, + ISSN = {2522-0160}, + MRCLASS = {11F55}, + MRNUMBER = {3667841}, + MRREVIEWER = {Mehmet Haluk \c{S}eng\"{u}n}, + DOI = {10.1007/s40993-017-0078-6}, + URL = {https://doi.org/10.1007/s40993-017-0078-6}, +} + +@article {Serre_Tate_Good_reduction, + AUTHOR = {Serre, J.-P. and Tate, J.}, + TITLE = {Good reduction of abelian varieties}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {88}, + YEAR = {1968}, + PAGES = {492--517}, + ISSN = {0003-486X}, + MRCLASS = {14.51}, + MRNUMBER = {236190}, + MRREVIEWER = {M. J. Greenberg}, + DOI = {10.2307/1970722}, + URL = {https://doi.org/10.2307/1970722}, +} + +@article {Landesman_Hyperelliptic_curves_maximal, + AUTHOR = {Landesman, A. and Swaminathan, A. A. and Tao, J. and + Xu, Y.}, + TITLE = {Hyperelliptic curves with maximal {G}alois action on the + torsion points of their {J}acobians}, + JOURNAL = {Indiana Univ. Math. J.}, + FJOURNAL = {Indiana University Mathematics Journal}, + VOLUME = {69}, + YEAR = {2020}, + NUMBER = {7}, + PAGES = {2461--2492}, + ISSN = {0022-2518}, + MRCLASS = {11G30 (11F80 11G10 11R32 14J40)}, + MRNUMBER = {4195609}, + DOI = {10.1512/iumj.2020.69.8178}, + URL = {https://doi.org/10.1512/iumj.2020.69.8178}, +} + +@article {Daniels_Hatley_Ricci_Elliptic_curves, + AUTHOR = {Daniels, H. B. and Hatley, J. and Ricci, J.}, + TITLE = {Elliptic curves with maximally disjoint division fields}, + JOURNAL = {Acta Arith.}, + FJOURNAL = {Acta Arithmetica}, + VOLUME = {175}, + YEAR = {2016}, + NUMBER = {3}, + PAGES = {211--223}, + ISSN = {0065-1036}, + MRCLASS = {14H52 (11F80)}, + MRNUMBER = {3557121}, + MRREVIEWER = {Rupam Barman}, + DOI = {10.4064/aa8275-7-2016}, + URL = {https://doi.org/10.4064/aa8275-7-2016}, +} + +@article {Jones_Gl2_reps, + AUTHOR = {Jones, N.}, + TITLE = {{${\rm GL}_2$}-representations with maximal image}, + JOURNAL = {Math. Res. Lett.}, + FJOURNAL = {Mathematical Research Letters}, + VOLUME = {22}, + YEAR = {2015}, + NUMBER = {3}, + PAGES = {803--839}, + ISSN = {1073-2780}, + MRCLASS = {11G05}, + MRNUMBER = {3350106}, + MRREVIEWER = {Hang Xue}, + DOI = {10.4310/MRL.2015.v22.n3.a10}, + URL = {https://doi.org/10.4310/MRL.2015.v22.n3.a10}, +} + +@article {Bleher_Poonen_Chinburg_Auto_HKG, + AUTHOR = {Bleher, F. M. and Chinburg, T. and Poonen, B. and + Symonds, P.}, + TITLE = {Automorphisms of {H}arbater-{K}atz-{G}abber curves}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {368}, + YEAR = {2017}, + NUMBER = {1-2}, + PAGES = {811--836}, + ISSN = {0025-5831}, + MRCLASS = {14H37 (14G17 20F29)}, + MRNUMBER = {3651589}, + MRREVIEWER = {Aristides I. Kontogeorgis}, + DOI = {10.1007/s00208-016-1490-2}, + URL = {https://doi.org/10.1007/s00208-016-1490-2}, +} + +@article {Chevalley_Weil_Uber_verhalten, + AUTHOR = {Chevalley, C. and Weil, A. and Hecke, E.}, + TITLE = {\"{U}ber das verhalten der integrale 1. gattung bei automorphismen + des funktionenk\"{o}rpers}, + JOURNAL = {Abh. Math. Sem. Univ. Hamburg}, + FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t + Hamburg}, + VOLUME = {10}, + YEAR = {1934}, + NUMBER = {1}, + PAGES = {358--361}, + ISSN = {0025-5858}, + MRCLASS = {DML}, + MRNUMBER = {3069638}, + DOI = {10.1007/BF02940687}, + URL = {https://doi.org/10.1007/BF02940687}, +} + + +@book {Hachenberger_Jungnickel_Topics, + AUTHOR = {Hachenberger, D. and Jungnickel, D.}, + TITLE = {Topics in {G}alois fields}, + SERIES = {Algorithms and Computation in Mathematics}, + VOLUME = {29}, + PUBLISHER = {Springer, Cham}, + YEAR = {[2020] \copyright 2020}, + PAGES = {xiv+785}, + ISBN = {978-3-030-60804-0; 978-3-030-60806-4}, + MRCLASS = {11Txx (12E20 12Fxx 15B33 94A55)}, + MRNUMBER = {4233161}, + DOI = {10.1007/978-3-030-60806-4}, + URL = {https://doi.org/10.1007/978-3-030-60806-4}, +} + +@article {Childs_Orzech_On_modular, + AUTHOR = {Childs, L. N. and Orzech, M.}, + TITLE = {On modular group rings, normal bases, and fixed points}, + JOURNAL = {Amer. Math. Monthly}, + FJOURNAL = {American Mathematical Monthly}, + VOLUME = {88}, + YEAR = {1981}, + NUMBER = {2}, + PAGES = {142--145}, + ISSN = {0002-9890}, + MRCLASS = {12F10}, + MRNUMBER = {606253}, + MRREVIEWER = {H. F. Kreimer}, + DOI = {10.2307/2321137}, + URL = {https://doi.org/10.2307/2321137}, +} + +@article {Poonen_Gonality_Modular, + AUTHOR = {Poonen, B.}, + TITLE = {Gonality of modular curves in characteristic {$p$}}, + JOURNAL = {Math. Res. Lett.}, + FJOURNAL = {Mathematical Research Letters}, + VOLUME = {14}, + YEAR = {2007}, + NUMBER = {4}, + PAGES = {691--701}, + ISSN = {1073-2780}, + MRCLASS = {11G18 (14G35 14H51)}, + MRNUMBER = {2335995}, + MRREVIEWER = {Am\'{\i}lcar Pacheco}, + DOI = {10.4310/MRL.2007.v14.n4.a14}, + URL = {https://doi.org/10.4310/MRL.2007.v14.n4.a14}, +} + +@article {Arbarello_Cornalba_Footnotes, + AUTHOR = {Arbarello, E. and Cornalba, M.}, + TITLE = {Footnotes to a paper of {B}eniamino {S}egre: ``{O}n the + modules of polygonal curves and on a complement to the + {R}iemann existence theorem'' ({I}talian) [{M}ath. {A}nn. {\bf + 100} (1928), 537--551; {J}buch {\bf 54}, 685]}, + JOURNAL = {Math. Ann.}, + FJOURNAL = {Mathematische Annalen}, + VOLUME = {256}, + YEAR = {1981}, + NUMBER = {3}, + PAGES = {341--362}, + ISSN = {0025-5831}, + MRCLASS = {14H10 (14H20)}, + MRNUMBER = {626954}, + MRREVIEWER = {Joseph Harris}, + DOI = {10.1007/BF01679702}, + URL = {https://doi.org/10.1007/BF01679702}, +} + +@misc{karanikolopoulos2010automorphisms, + title={{A}utomorphisms of {C}urves and {W}eierstrass semigroups}, + author={Karanikolopoulos, S. and Kontogeorgis, A.}, + year={2010}, + eprint={1005.2871}, + archivePrefix={arXiv}, + primaryClass={math.AG}, + note={unpublished}, +} + +@article {Saltman_Noncrossed_product, + AUTHOR = {Saltman, D. J.}, + TITLE = {Noncrossed product {$p$}-algebras and {G}alois + {$p$}-extensions}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {52}, + YEAR = {1978}, + NUMBER = {2}, + PAGES = {302--314}, + ISSN = {0021-8693}, + MRCLASS = {16A74 (12A80 12G05)}, + MRNUMBER = {480640}, + MRREVIEWER = {M. E. Keating}, + DOI = {10.1016/0021-8693(78)90240-5}, + URL = {https://doi.org/10.1016/0021-8693(78)90240-5}, +} + +@article {Valentini_Madan_Automorphisms, + AUTHOR = {Valentini, R. C. and Madan, M. L.}, + TITLE = {Automorphisms and holomorphic differentials in characteristic~{$p$}}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {13}, + YEAR = {1981}, + NUMBER = {1}, + PAGES = {106--115}, + ISSN = {0022-314X}, + MRCLASS = {14F10}, + MRNUMBER = {602451}, + DOI = {10.1016/0022-314X(81)90032-9}, + URL = {https://doi.org/10.1016/0022-314X(81)90032-9}, +} + +@book {Webb_finite_group_representations, + AUTHOR = {Webb, P.}, + TITLE = {A course in finite group representation theory}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {161}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2016}, + PAGES = {xi+325}, + ISBN = {978-1-107-16239-6}, + MRCLASS = {20-02 (20C05)}, + MRNUMBER = {3617363}, + MRREVIEWER = {Stuart Martin}, + DOI = {10.1017/CBO9781316677216}, + URL = {https://doi.org/10.1017/CBO9781316677216}, +} + +@book {Dornhoff_modular_representation_theory, + AUTHOR = {Dornhoff, L.}, + TITLE = {Group representation theory. {P}art {B}: {M}odular + representation theory}, + SERIES = {Pure and Applied Mathematics}, + VOLUME = {7}, + PUBLISHER = {Marcel Dekker, Inc., New York}, + YEAR = {1972}, + PAGES = {vii+pp. 255--511}, + MRCLASS = {20C15 (20C20)}, + MRNUMBER = {0347960}, + MRREVIEWER = {A. Dress}, +} + +@book {Mollin_ANT, + AUTHOR = {Mollin, R. A.}, + TITLE = {Algebraic number theory}, + SERIES = {Discrete Mathematics and its Applications (Boca Raton)}, + EDITION = {Second}, + PUBLISHER = {CRC Press, Boca Raton, FL}, + YEAR = {2011}, + PAGES = {xvi+426}, + ISBN = {978-1-4398-4598-1}, + MRCLASS = {11-03 (11Rxx)}, + MRNUMBER = {2779314}, + DOI = {10.1201/b10493}, + URL = {https://doi.org/10.1201/b10493}, +} + +@article {Elder_valuation_criterion_positive_char, + AUTHOR = {Elder, G. G.}, + TITLE = {A valuation criterion for normal basis generators in local + fields of characteristic {$p$}}, + JOURNAL = {Arch. Math. (Basel)}, + FJOURNAL = {Archiv der Mathematik}, + VOLUME = {94}, + YEAR = {2010}, + NUMBER = {1}, + PAGES = {43--47}, + ISSN = {0003-889X}, + MRCLASS = {11S15 (12J10)}, + MRNUMBER = {2581332}, + MRREVIEWER = {Martha Rzedowski-Calder\'{o}n}, + DOI = {10.1007/s00013-009-0076-6}, + URL = {https://doi.org/10.1007/s00013-009-0076-6}, +} + +@article {Valuation_criterion_normal_basis, + AUTHOR = {de Smit, B. and Florence, M. and Thomas, L.}, + TITLE = {The valuation criterion for normal basis generators}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {44}, + YEAR = {2012}, + NUMBER = {4}, + PAGES = {729--737}, + ISSN = {0024-6093}, + MRCLASS = {11S20 (20C05)}, + MRNUMBER = {2967240}, + MRREVIEWER = {G. Griffith Elder}, + DOI = {10.1112/blms/bds005}, + URL = {https://doi.org/10.1112/blms/bds005}, +} + +@article {Harbater_moduli_of_p_covers, + AUTHOR = {Harbater, D.}, + TITLE = {Moduli of {$p$}-covers of curves}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {8}, + YEAR = {1980}, + NUMBER = {12}, + PAGES = {1095--1122}, + ISSN = {0092-7872}, + MRCLASS = {14D15 (14H30)}, + MRNUMBER = {579791}, + MRREVIEWER = {David Cox}, + DOI = {10.1080/00927878008822511}, + URL = {https://doi.org/10.1080/00927878008822511}, +} + +@article {Bleher_Chinburg_Kontogeorgis_Galois_structure, + AUTHOR = {Bleher, F. M. and Chinburg, T. and Kontogeorgis, + A.}, + TITLE = {Galois structure of the holomorphic differentials of curves}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {216}, + YEAR = {2020}, + PAGES = {1--68}, + ISSN = {0022-314X}, + MRCLASS = {14G35 (11G20 14G17 14H05 20C20)}, + MRNUMBER = {4130074}, + DOI = {10.1016/j.jnt.2020.04.015}, + URL = {https://doi.org/10.1016/j.jnt.2020.04.015}, +} + +@article {Nakajima_Galois_module, + AUTHOR = {Nakajima, S.}, + TITLE = {Galois module structure of cohomology groups for tamely + ramified coverings of algebraic varieties}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {22}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {115--123}, + ISSN = {0022-314X}, + MRCLASS = {14E20 (11R34 14E40)}, + MRNUMBER = {821138}, + MRREVIEWER = {Lindsay N. Childs}, + DOI = {10.1016/0022-314X(86)90032-6}, + URL = {https://doi.org/10.1016/0022-314X(86)90032-6}, +} + +@article {Kani_Galois_module, + AUTHOR = {Kani, E.}, + TITLE = {The {G}alois-module structure of the space of holomorphic + differentials of a curve}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {367}, + YEAR = {1986}, + PAGES = {187--206}, + ISSN = {0075-4102}, + MRCLASS = {14H05 (14F10 14H30)}, + MRNUMBER = {839131}, + MRREVIEWER = {Shoichi Nakajima}, + DOI = {10.1515/crll.1986.367.187}, + URL = {https://doi.org/10.1515/crll.1986.367.187}, +} + +@book {Washington_Intro_to_cyclotomic, + AUTHOR = {Washington, L. C.}, + TITLE = {Introduction to cyclotomic fields}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {83}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1997}, + PAGES = {xiv+487}, + ISBN = {0-387-94762-0}, + MRCLASS = {11R18 (11-01 11-02 11R23)}, + MRNUMBER = {1421575}, + MRREVIEWER = {T. Mets\"{a}nkyl\"{a}}, + DOI = {10.1007/978-1-4612-1934-7}, + URL = {https://doi.org/10.1007/978-1-4612-1934-7}, +} + +@article {Huynh_Artin_Schreier_extensions, + AUTHOR = {Huynh, D. V.}, + TITLE = {Artin-{S}chreier extensions and generalized associated orders}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {136}, + YEAR = {2014}, + PAGES = {28--45}, + ISSN = {0022-314X}, + MRCLASS = {11R33 (11S15)}, + MRNUMBER = {3145322}, + MRREVIEWER = {Nigel Byott}, + DOI = {10.1016/j.jnt.2013.09.009}, + URL = {https://doi.org/10.1016/j.jnt.2013.09.009}, +} + +@article {Tate_residues_differentials_curves, + AUTHOR = {Tate, J.}, + TITLE = {Residues of differentials on curves}, + JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme + S\'{e}rie}, + VOLUME = {1}, + YEAR = {1968}, + PAGES = {149--159}, + ISSN = {0012-9593}, + MRCLASS = {14.20}, + MRNUMBER = {227171}, + MRREVIEWER = {R. L. Knighten}, + URL = {http://www.numdam.org/item?id=ASENS_1968_4_1_1_149_0}, +} + +@incollection {Hubl_residual_representation, + AUTHOR = {H\"{u}bl, R.}, + TITLE = {Residual representation of algebraic-geometric codes}, + NOTE = {Effective methods in algebraic and analytic geometry, 2000 + (Krak\'{o}w)}, + JOURNAL = {Univ. Iagel. Acta Math.}, + FJOURNAL = {Universitatis Iagellonicae. Acta Mathematica}, + NUMBER = {39}, + YEAR = {2001}, + PAGES = {25--48}, + ISSN = {0083-4386}, + MRCLASS = {14G50 (14F10 94B27)}, + MRNUMBER = {1886927}, + MRREVIEWER = {Peter Br\"{u}ckmann}, +} + +@article {Zannier_traces_diff_forms, + AUTHOR = {Zannier, U.}, + TITLE = {A note on traces of differential forms}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {142}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {91--97}, + ISSN = {0022-4049}, + MRCLASS = {13N05 (14F10)}, + MRNUMBER = {1716049}, + MRREVIEWER = {Reinhold H\"{u}bl}, + DOI = {10.1016/S0022-4049(98)00045-0}, + URL = {https://doi.org/10.1016/S0022-4049(98)00045-0}, +} + + +@article {Kock_galois_structure, + AUTHOR = {K\"{o}ck, B.}, + TITLE = {Galois structure of {Z}ariski cohomology for weakly ramified + covers of curves}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {126}, + YEAR = {2004}, + NUMBER = {5}, + PAGES = {1085--1107}, + ISSN = {0002-9327}, + MRCLASS = {11R33 (11G30 14H30)}, + MRNUMBER = {2089083}, + MRREVIEWER = {Nigel Byott}, + URL = + {http://muse.jhu.edu/journals/american_journal_of_mathematics/v126/126.5k"ock.pdf}, +} + +@article {WardMarques_HoloDiffs, + AUTHOR = {Marques, S. and Ward, K.}, + TITLE = {Holomorphic differentials of certain solvable covers of the + projective line over a perfect field}, + JOURNAL = {Math. Nachr.}, + FJOURNAL = {Mathematische Nachrichten}, + VOLUME = {291}, + YEAR = {2018}, + NUMBER = {13}, + PAGES = {2057--2083}, + ISSN = {0025-584X}, + MRCLASS = {11G20 (11R58 14H05)}, + MRNUMBER = {3858677}, + MRREVIEWER = {Valentijn Zo\"{e} Karemaker}, + DOI = {10.1002/mana.201500347}, + URL = {https://doi.org/10.1002/mana.201500347}, +} + +@article {CasselsSchinzel_Selmers_conjecture, + AUTHOR = {Cassels, J. W. S. and Schinzel, A.}, + TITLE = {Selmer's conjecture and families of elliptic curves}, + JOURNAL = {Bull. London Math. Soc.}, + FJOURNAL = {The Bulletin of the London Mathematical Society}, + VOLUME = {14}, + YEAR = {1982}, + NUMBER = {4}, + PAGES = {345--348}, + ISSN = {0024-6093}, + MRCLASS = {14K07 (10B10 14G05)}, + MRNUMBER = {663485}, + MRREVIEWER = {M. Bashmakov}, + DOI = {10.1112/blms/14.4.345}, + URL = {https://doi.org/10.1112/blms/14.4.345}, +} + +@book {szamuely_galois_fundamental, + AUTHOR = {Szamuely, T.}, + TITLE = {Galois groups and fundamental groups}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {117}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2009}, + PAGES = {x+270}, + ISBN = {978-0-521-88850-9}, + MRCLASS = {14H30 (11-02 12F10 14G32)}, + MRNUMBER = {2548205}, + MRREVIEWER = {Swaminathan Subramanian}, + DOI = {10.1017/CBO9780511627064}, + URL = {https://doi.org/10.1017/CBO9780511627064}, +} + +@article {harbater_stevenson_patching_thickening, + AUTHOR = {Harbater, D. and Stevenson, K. F.}, + TITLE = {Patching and thickening problems}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {212}, + YEAR = {1999}, + NUMBER = {1}, + PAGES = {272--304}, + ISSN = {0021-8693}, + MRCLASS = {14B10 (12F12 14B12 14H30)}, + MRNUMBER = {1670658}, + MRREVIEWER = {Hiroaki Nakamura}, + DOI = {10.1006/jabr.1998.7574}, + URL = {https://doi.org/10.1006/jabr.1998.7574}, +} + +@article {chinburg_epsilon_constants, + AUTHOR = {Chinburg, T. and Erez, B. and Pappas, G. and Taylor, + M. J.}, + TITLE = {{$\epsilon$}-constants and the {G}alois structure of de {R}ham + cohomology}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {146}, + YEAR = {1997}, + NUMBER = {2}, + PAGES = {411--473}, + ISSN = {0003-486X}, + MRCLASS = {14F40 (11G09 11R33)}, + MRNUMBER = {1477762}, + MRREVIEWER = {Nigel Byott}, + DOI = {10.2307/2952466}, + URL = {https://doi.org/10.2307/2952466}, +} + +@article {apostol_resultant_cyclotomic, + AUTHOR = {Apostol, T. M.}, + TITLE = {Resultants of cyclotomic polynomials}, + JOURNAL = {Proc. Amer. Math. Soc.}, + FJOURNAL = {Proceedings of the American Mathematical Society}, + VOLUME = {24}, + YEAR = {1970}, + PAGES = {457--462}, + ISSN = {0002-9939}, + MRCLASS = {10.76}, + MRNUMBER = {251010}, + MRREVIEWER = {L. Carlitz}, + DOI = {10.2307/2037387}, + URL = {https://doi.org/10.2307/2037387}, +} + +@incollection {divisibility_l_polynomials, + AUTHOR = {Blanco-Chac\'{o}n, I. and Chapman, R. and Fordham, S. and McGuire, + G.}, + TITLE = {Divisibility of {L}-polynomials for a family of curves}, + BOOKTITLE = {Contemporary developments in finite fields and applications}, + PAGES = {1--10}, + PUBLISHER = {World Sci. Publ., Hackensack, NJ}, + YEAR = {2016}, + MRCLASS = {11T06 (11T23)}, + MRNUMBER = {3587254}, + MRREVIEWER = {Alina Ostafe}, +} + +@article {divisibility_l_polynomials_as, + AUTHOR = {McGuire, G. and Y\i lmaz, E. S.}, + TITLE = {Divisibility of {L}-polynomials for a family of + {A}rtin-{S}chreier curves}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {223}, + YEAR = {2019}, + NUMBER = {8}, + PAGES = {3341--3358}, + ISSN = {0022-4049}, + MRCLASS = {11G20 (14H05)}, + MRNUMBER = {3926215}, + MRREVIEWER = {Yves Aubry}, + DOI = {10.1016/j.jpaa.2018.11.005}, + URL = {https://doi.org/10.1016/j.jpaa.2018.11.005}, +} + +@article {further_cross_correlation, + AUTHOR = {Johansen, A. and Helleseth, T. and Kholosha, A.}, + TITLE = {Further results on {$m$}-sequences with five-valued cross + correlation}, + JOURNAL = {IEEE Trans. Inform. Theory}, + FJOURNAL = {Institute of Electrical and Electronics Engineers. + Transactions on Information Theory}, + VOLUME = {55}, + YEAR = {2009}, + NUMBER = {12}, + PAGES = {5792--5802}, + ISSN = {0018-9448}, + MRCLASS = {94A55}, + MRNUMBER = {2597195}, + DOI = {10.1109/TIT.2009.2032854}, + URL = {https://doi.org/10.1109/TIT.2009.2032854}, +} + +@article {decomposing_jacobians, + AUTHOR = {Ahmadi, O. and McGuire, G. and Rojas-Le\'{o}n, A.}, + TITLE = {Decomposing {J}acobians of curves over finite fields in the + absence of algebraic structure}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {156}, + YEAR = {2015}, + PAGES = {414--431}, + ISSN = {0022-314X}, + MRCLASS = {14G15 (11M38 14G10)}, + MRNUMBER = {3360347}, + MRREVIEWER = {Yves Aubry}, + DOI = {10.1016/j.jnt.2015.04.014}, + URL = {https://doi.org/10.1016/j.jnt.2015.04.014}, +} + +@article {Kock_galois_structure, + AUTHOR = {K\"{o}ck, B.}, + TITLE = {Galois structure of {Z}ariski cohomology for weakly ramified + covers of curves}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {126}, + YEAR = {2004}, + NUMBER = {5}, + PAGES = {1085--1107}, + ISSN = {0002-9327}, + MRCLASS = {11R33 (11G30 14H30)}, + MRNUMBER = {2089083}, + MRREVIEWER = {Nigel Byott}, + URL = + {http://muse.jhu.edu/journals/american_journal_of_mathematics/v126/126.5k"ock.pdf}, +} + +@article {elkin_pries_ekedahl_oort, + AUTHOR = {Elkin, A. and Pries, R.}, + TITLE = {Ekedahl-{O}ort strata of hyperelliptic curves in + characteristic 2}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {7}, + YEAR = {2013}, + NUMBER = {3}, + PAGES = {507--532}, + ISSN = {1937-0652}, + MRCLASS = {11G30 (14G17 14H45)}, + MRNUMBER = {3095219}, + MRREVIEWER = {Fabien Pazuki}, + DOI = {10.2140/ant.2013.7.507}, + URL = {https://doi.org/10.2140/ant.2013.7.507}, +} + +@article {achinger_wild_ramification, + AUTHOR = {Achinger, P.}, + TITLE = {Wild ramification and {$K(\pi, 1)$} spaces}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {210}, + YEAR = {2017}, + NUMBER = {2}, + PAGES = {453--499}, + ISSN = {0020-9910}, + MRCLASS = {14F35 (14F20 14G22 14R10)}, + MRNUMBER = {3714509}, + MRREVIEWER = {Enlin Yang}, + DOI = {10.1007/s00222-017-0733-5}, + URL = {https://doi.org/10.1007/s00222-017-0733-5}, +} + +@article{Ohshita2020, + title = "Asymptotic lower bound of class numbers along a {G}alois representation", + journal = "Journal of Number Theory", + volume = "211", + pages = "95 - 112", + year = "2020", + issn = "0022-314X", + doi = "https://doi.org/10.1016/j.jnt.2019.09.024", + url = "http://www.sciencedirect.com/science/article/pii/S0022314X19303567", + author = "Ohshita, T.", +} + +@book{Hindry_Silverman, + AUTHOR = {Hindry, M. and Silverman, J. H.}, + TITLE = {Diophantine geometry}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {201}, + NOTE = {An introduction}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {2000}, + PAGES = {xiv+558}, + ISBN = {0-387-98975-7; 0-387-98981-1}, + MRCLASS = {11Gxx (11-02 11G10 11G30 11G50 14G25)}, + MRNUMBER = {1745599}, + MRREVIEWER = {Dino J. Lorenzini}, + DOI = {10.1007/978-1-4612-1210-2}, + URL = {https://doi.org/10.1007/978-1-4612-1210-2}, +} + +@book{Lan_arithmetic_compactifications, + AUTHOR = {Lan, K.-W,}, + TITLE = {Arithmetic compactifications of {PEL}-type {S}himura + varieties}, + SERIES = {London Mathematical Society Monographs Series}, + VOLUME = {36}, + PUBLISHER = {Princeton University Press, Princeton, NJ}, + YEAR = {2013}, + PAGES = {xxvi+561}, + ISBN = {978-0-691-15654-5}, + MRCLASS = {14G35 (11G18 14D23 14M27)}, + MRNUMBER = {3186092}, + MRREVIEWER = {Rolf Berndt}, + DOI = {10.1515/9781400846016}, + URL = {https://doi.org/10.1515/9781400846016}, +} + +@article {Clark_Xarles_local_bounds, + AUTHOR = {Clark, P. L. and Xarles, X.}, + TITLE = {Local bounds for torsion points on abelian varieties}, + JOURNAL = {Canad. J. Math.}, + FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de + Math\'{e}matiques}, + VOLUME = {60}, + YEAR = {2008}, + NUMBER = {3}, + PAGES = {532--555}, + ISSN = {0008-414X}, + MRCLASS = {11G10 (11G25 14K15)}, + MRNUMBER = {2414956}, + MRREVIEWER = {Ivica Gusi\'{c}}, + DOI = {10.4153/CJM-2008-026-x}, + URL = {https://doi.org/10.4153/CJM-2008-026-x}, +} + +@article {Oort_CM_liftings, + AUTHOR = {Oort, F.}, + TITLE = {C{M}-liftings of abelian varieties}, + JOURNAL = {J. Algebraic Geom.}, + FJOURNAL = {Journal of Algebraic Geometry}, + VOLUME = {1}, + YEAR = {1992}, + NUMBER = {1}, + PAGES = {131--146}, + ISSN = {1056-3911}, + MRCLASS = {14K22 (14K15)}, + MRNUMBER = {1129842}, + MRREVIEWER = {Min Ho Lee}, +} + +@book {Chai_Conrad_CM_and_lifting_problems, + AUTHOR = {Chai, Ch.-L. and Conrad, B. and Oort, F.}, + TITLE = {Complex multiplication and lifting problems}, + SERIES = {Mathematical Surveys and Monographs}, + VOLUME = {195}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2014}, + PAGES = {x+387}, + ISBN = {978-1-4704-1014-8}, + MRCLASS = {14K22 (11G15 14D15 14K02 14K15 14L05)}, + MRNUMBER = {3137398}, + MRREVIEWER = {Mihran Papikian}, +} + +@article {Raynaud_schemas_ppp, + AUTHOR = {Raynaud, M.}, + TITLE = {Sch\'{e}mas en groupes de type {$(p,\dots, p)$}}, + JOURNAL = {Bull. Soc. Math. France}, + FJOURNAL = {Bulletin de la Soci\'{e}t\'{e} Math\'{e}matique de France}, + VOLUME = {102}, + YEAR = {1974}, + PAGES = {241--280}, + ISSN = {0037-9484}, + MRCLASS = {14L20 (14L25)}, + MRNUMBER = {419467}, + MRREVIEWER = {F. Oort}, + URL = {http://www.numdam.org/item?id=BSMF_1974__102__241_0}, +} + +@article {Hortsch_canonical_representation, + AUTHOR = {Hortsch, R.}, + TITLE = {On the canonical representation of curves in positive + characteristic}, + JOURNAL = {New York J. Math.}, + FJOURNAL = {New York Journal of Mathematics}, + VOLUME = {18}, + YEAR = {2012}, + PAGES = {911--924}, + MRCLASS = {14G17 (11G05)}, + MRNUMBER = {3007205}, + MRREVIEWER = {Rachel J. Pries}, + URL = {http://nyjm.albany.edu:8000/j/2012/18_911.html}, +} + +@article{Ishii_trace, + title={Trace of {F}robenius endomorphism of an elliptic curve with complex multiplication}, + volume={70}, + DOI={10.1017/S0004972700035875}, + number={1}, + journal={Bulletin of the Australian Mathematical Society}, + publisher={Cambridge University Press}, + author={Ishii, N.}, + year={2004}, + pages={125--142} +} + +@article {Conrad_Chevalley, + AUTHOR = {Conrad, B.}, + TITLE = {A modern proof of {C}hevalley's theorem on algebraic groups}, + JOURNAL = {J. Ramanujan Math. Soc.}, + FJOURNAL = {Journal of the Ramanujan Mathematical Society}, + VOLUME = {17}, + YEAR = {2002}, + NUMBER = {1}, + PAGES = {1--18}, + ISSN = {0970-1249}, + MRCLASS = {20G15 (11H99 14K05 14L15)}, + MRNUMBER = {1906417}, + MRREVIEWER = {James E. Humphreys}, +} + +@book {Stichtenoth_algebraic_function_fields, + AUTHOR = {Stichtenoth, H.}, + TITLE = {Algebraic function fields and codes}, + SERIES = {Universitext}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1993}, + PAGES = {x+260}, + ISBN = {3-540-56489-6}, + MRCLASS = {14H05 (11R58 11T71 14G15 94B27)}, + MRNUMBER = {1251961}, + MRREVIEWER = {R. F. Lax}, +} + +@incollection {Pries_short_guide, + AUTHOR = {Pries, R.}, + TITLE = {A short guide to {$p$}-torsion of abelian varieties in + characteristic {$p$}}, + BOOKTITLE = {Computational arithmetic geometry}, + SERIES = {Contemp. Math.}, + VOLUME = {463}, + PAGES = {121--129}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {2008}, + MRCLASS = {11G15 (11G10 14K10)}, + MRNUMBER = {2459994}, + MRREVIEWER = {Adrian Vasiu}, + DOI = {10.1090/conm/463/09051}, + URL = {https://doi.org/10.1090/conm/463/09051}, +} + +@book {FWGSS1986, + AUTHOR = {Faltings, G. and W\"ustholz, G. and Grunewald, F. and + Schappacher, N. and Stuhler, U.}, + TITLE = {Rational points}, + SERIES = {Aspects of Mathematics, E6}, + EDITION = {Second}, + NOTE = {Papers from the seminar held at the Max-Planck-Institut f\"ur + Mathematik, Bonn/Wuppertal, 1983/1984}, + PUBLISHER = {Friedr. Vieweg \& Sohn, Braunschweig}, + YEAR = {1986}, + PAGES = {vi+268}, + ISBN = {3-528-18593-7}, + MRCLASS = {11D41 (11G35 14G05 14H25 14K15)}, + MRNUMBER = {863887}, + URL = {https://doi.org/10.1007/978-3-663-06812-9}, +} + +@article {Zarhin1985, + AUTHOR = {Zarhin, Yu. G.}, + TITLE = {A finiteness theorem for unpolarized abelian varieties over + number fields with prescribed places of bad reduction}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {79}, + YEAR = {1985}, + NUMBER = {2}, + PAGES = {309--321}, + ISSN = {0020-9910}, + MRCLASS = {14K15 (11G10)}, + MRNUMBER = {778130}, + MRREVIEWER = {Gerd Faltings}, + URL = {https://doi.org/10.1007/BF01388976}, +} + +@article {JiQin_CM_elliptic_curves_and_primes, + AUTHOR = {Ji, Q. and Qin, H.}, + TITLE = {C{M} elliptic curves and primes captured by quadratic + polynomials}, + JOURNAL = {Asian J. Math.}, + FJOURNAL = {Asian Journal of Mathematics}, + VOLUME = {18}, + YEAR = {2014}, + NUMBER = {4}, + PAGES = {707--726}, + ISSN = {1093-6106}, + MRCLASS = {11N32 (11G05 11G15)}, + MRNUMBER = {3275725}, + MRREVIEWER = {Jordi Gu\`ardia}, + DOI = {10.4310/AJM.2014.v18.n4.a7}, + URL = {https://doi.org/10.4310/AJM.2014.v18.n4.a7}, +} + +@incollection {JongNoot_jacobians, + AUTHOR = {de Jong, J. and Noot, R.}, + TITLE = {Jacobians with complex multiplication}, + BOOKTITLE = {Arithmetic algebraic geometry ({T}exel, 1989)}, + SERIES = {Progr. Math.}, + VOLUME = {89}, + PAGES = {177--192}, + PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, + YEAR = {1991}, + MRCLASS = {11G15 (14G35 14H40)}, + MRNUMBER = {1085259}, + MRREVIEWER = {Ehud de Shalit}, +} + +@article {Blake_deuring_criterion, + AUTHOR = {Blake, C.}, + TITLE = {A {D}euring criterion for abelian varieties}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {46}, + YEAR = {2014}, + NUMBER = {6}, + PAGES = {1256--1263}, + ISSN = {0024-6093}, + MRCLASS = {11G10 (11G15)}, + MRNUMBER = {3291261}, + MRREVIEWER = {James H. Stankewicz}, + DOI = {10.1112/blms/bdu079}, + URL = {https://doi.org/10.1112/blms/bdu079}, +} + +@article {JouxMorain95, + AUTHOR = {Joux, A. and Morain, F.}, + TITLE = {Sur les sommes de caract\`eres li\'{e}es aux courbes elliptiques \`a + multiplication complexe}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {55}, + YEAR = {1995}, + NUMBER = {1}, + PAGES = {108--128}, + ISSN = {0022-314X}, + MRCLASS = {11L10 (11G05 11L40)}, + MRNUMBER = {1361563}, + MRREVIEWER = {Dimitrios Poulakis}, + DOI = {10.1006/jnth.1995.1131}, + URL = {https://doi.org/10.1006/jnth.1995.1131}, +} + +@book {EGAIII, + AUTHOR = {Grothendieck, A. and Dieudonn\'{e}, J. A.}, + TITLE = {El\'{e}ments de g\'{e}om\'{e}trie alg\'{e}brique. {III}}, + SERIES = {Pub. Math. IHES}, + VOLUME = {166}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1971}, + PAGES = {ix+466}, + ISBN = {3-540-05113-9; 0-387-05113-9}, + MRCLASS = {14-02 (14A15 14F05)}, + MRNUMBER = {3075000}, +} + +@book {Neukirch_ANT, + AUTHOR = {Neukirch, J.}, + TITLE = {Algebraic number theory}, + SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental + Principles of Mathematical Sciences]}, + VOLUME = {322}, + NOTE = {Translated from the 1992 German original and with a note by + Norbert Schappacher, + With a foreword by G. Harder}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1999}, + PAGES = {xviii+571}, + ISBN = {3-540-65399-6}, + MRCLASS = {11Rxx (11-02 11S15 11S31 14C40)}, + MRNUMBER = {1697859}, + MRREVIEWER = {Cornelius Greither}, + DOI = {10.1007/978-3-662-03983-0}, + URL = {https://doi.org/10.1007/978-3-662-03983-0}, +} + +@article {Qin_anomalous, + AUTHOR = {Qin, H.}, + TITLE = {Anomalous primes of the elliptic curve {$E_D\colon + y^2=x^3+D$}}, + JOURNAL = {Proc. Lond. Math. Soc. (3)}, + FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, + VOLUME = {112}, + YEAR = {2016}, + NUMBER = {2}, + PAGES = {415--453}, + ISSN = {0024-6115}, + MRCLASS = {11G05 (11G15 11R09 14G25)}, + MRNUMBER = {3471254}, + MRREVIEWER = {Matthew A. Papanikolas}, + DOI = {10.1112/plms/pdv072}, + URL = {https://doi.org/10.1112/plms/pdv072}, +} + +@article {Sutherland_computing_images, + AUTHOR = {Sutherland, A. V.}, + TITLE = {Computing images of {G}alois representations attached to + elliptic curves}, + JOURNAL = {Forum Math. Sigma}, + FJOURNAL = {Forum of Mathematics. Sigma}, + VOLUME = {4}, + YEAR = {2016}, + PAGES = {e4, 79}, + MRCLASS = {11G05 (11F80 11G20 11Y16)}, + MRNUMBER = {3482279}, +MRREVIEWER = {Susan L. Schmoyer}, + DOI = {10.1017/fms.2015.33}, + URL = {https://doi.org/10.1017/fms.2015.33}, +} + +@article {Cartier_nouvelle_operation, + AUTHOR = {Cartier, P.}, + TITLE = {Une nouvelle op\'{e}ration sur les formes diff\'{e}rentielles}, + JOURNAL = {C. R. Acad. Sci. Paris}, + FJOURNAL = {Comptes Rendus Hebdomadaires des S\'{e}ances de l'Acad\'{e}mie des + Sciences}, + VOLUME = {244}, + YEAR = {1957}, + PAGES = {426--428}, + ISSN = {0001-4036}, + MRCLASS = {09.3X}, + MRNUMBER = {84497}, +MRREVIEWER = {T. Nakayama}, +} + +@misc{achinger2017liftability, + title={Liftability of the {F}robenius morphism and images of toric varieties}, + author={Achinger, P. and Witaszek, J. and Zdanowicz, M.}, + year={2017}, + eprint={1708.03777}, + archivePrefix={arXiv}, + primaryClass={math.AG} +} + +@article {Oda_first_de_rham, + AUTHOR = {Oda, T.}, + TITLE = {The first de {R}ham cohomology group and {D}ieudonn\'{e} modules}, + JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme + S\'{e}rie}, + VOLUME = {2}, + YEAR = {1969}, + PAGES = {63--135}, + ISSN = {0012-9593}, + MRCLASS = {14.55}, + MRNUMBER = {0241435}, +MRREVIEWER = {J. S. Milne}, + URL = {http://www.numdam.org/item?id=ASENS_1969_4_2_1_63_0}, +} + +@book {Voisin_hodge_book_I, + AUTHOR = {Voisin, C.}, + TITLE = {Hodge theory and complex algebraic geometry. {I}}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {76}, + NOTE = {Translated from the French original by Leila Schneps}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2002}, + PAGES = {x+322}, + ISBN = {0-521-80260-1}, + MRCLASS = {32J25 (14C30 14D07 32G20)}, + MRNUMBER = {1967689}, +MRREVIEWER = {Javier A. Fern\'{a}ndez}, + DOI = {10.1017/CBO9780511615344}, + URL = {https://doi.org/10.1017/CBO9780511615344}, +} + +@article {Garnek_equivariant, + AUTHOR = {Garnek, J.}, + TITLE = {Equivariant splitting of the {H}odge-de {R}ham exact sequence}, + JOURNAL = {Math. Z.}, + FJOURNAL = {Mathematische Zeitschrift}, + VOLUME = {300}, + YEAR = {2022}, + NUMBER = {2}, + PAGES = {1917--1938}, + ISSN = {0025-5874}, + MRCLASS = {14F40 (14G17 14H37)}, + MRNUMBER = {4363802}, + DOI = {10.1007/s00209-021-02839-y}, + URL = {https://doi.org/10.1007/s00209-021-02839-y}, +} + +@article {Garnek_class_numbers, + AUTHOR = {Garnek, J.}, + TITLE = {On class numbers of division fields of abelian varieties}, + JOURNAL = {J. Th\'eor. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux}, + VOLUME = {31}, + YEAR = {2019}, + NUMBER = {1}, + PAGES = {227--242}, +} + +@article {Kummer_waluacja_symbolu, + AUTHOR = {Kummer, E. E.}, + TITLE = {\"{U}ber die {E}rg\"{a}nzungss\"{a}tze zu den allgemeinen + {R}eciprocit\"{a}tsgesetzen}, + JOURNAL = {J. Reine Angew. Math.}, + FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's + Journal]}, + VOLUME = {44}, + YEAR = {1852}, + PAGES = {93--146}, + ISSN = {0075-4102}, + MRCLASS = {DML}, + MRNUMBER = {1578793}, + DOI = {10.1515/crll.1852.44.93}, + URL = {https://doi.org/10.1515/crll.1852.44.93}, +} + +@article {Nakajima_Automorphism, + AUTHOR = {Nakajima, S.}, + TITLE = {Action of an automorphism of order {$p$} on cohomology groups + of an algebraic curve}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {42}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {85--94}, + ISSN = {0022-4049}, + MRCLASS = {14H30 (14E20)}, + MRNUMBER = {852320}, +MRREVIEWER = {K. Kiyek}, + DOI = {10.1016/0022-4049(86)90062-9}, + URL = {https://doi.org/10.1016/0022-4049(86)90062-9}, +} + +@article {Pop_OortConjecture, + AUTHOR = {Pop, F.}, + TITLE = {The {O}ort conjecture on lifting covers of curves}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {180}, + YEAR = {2014}, + NUMBER = {1}, + PAGES = {285--322}, + ISSN = {0003-486X}, + MRCLASS = {11G05 (11S15 14G32)}, + MRNUMBER = {3194816}, +MRREVIEWER = {Konstantinos Draziotis}, + DOI = {10.4007/annals.2014.180.1.6}, + URL = {https://doi.org/10.4007/annals.2014.180.1.6}, +} + +@book {Messing_Crystals, + AUTHOR = {Messing, W.}, + TITLE = {The crystals associated to {B}arsotti-{T}ate groups: with + applications to abelian schemes}, + SERIES = {Lecture Notes in Mathematics, Vol. 264}, + PUBLISHER = {Springer-Verlag, Berlin-New York}, + YEAR = {1972}, + PAGES = {iii+190}, + MRCLASS = {14L05 (14B20 14D15 14F30 14K10)}, + MRNUMBER = {0347836}, +MRREVIEWER = {F. Oort}, +} + +@article {CornelissenKato2003, + AUTHOR = {Cornelissen, G. and Kato, F.}, + TITLE = {Equivariant deformation of {M}umford curves and of ordinary + curves in positive characteristic}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {116}, + YEAR = {2003}, + NUMBER = {3}, + PAGES = {431--470}, + ISSN = {0012-7094}, + MRCLASS = {14G22 (14D15 14H37)}, + MRNUMBER = {1958094}, +MRREVIEWER = {Letterio Gatto}, + DOI = {10.1215/S0012-7094-03-11632-4}, + URL = {https://doi.org/10.1215/S0012-7094-03-11632-4}, +} + +@article {KronbergSoomroTop, + AUTHOR = {Kronberg, M. and Soomro, M. A. and Top, J.}, + TITLE = {Twists of elliptic curves}, + JOURNAL = {SIGMA Symmetry Integrability Geom. Methods Appl.}, + FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and + Applications}, + VOLUME = {13}, + YEAR = {2017}, + PAGES = {Paper No. 083, 13}, + ISSN = {1815-0659}, + MRCLASS = {11G05 (11G25 14G17 14H52)}, + MRNUMBER = {3715838}, +MRREVIEWER = {Nathan Kaplan}, + DOI = {10.3842/SIGMA.2017.083}, + URL = {https://doi.org/10.3842/SIGMA.2017.083}, +} + +@misc{Milne_AVs, +author={Milne, J. S.}, +title={Abelian Varieties (v2.00)}, +year={2008}, +note={Available at www.jmilne.org/math/}, +pages={166+vi} +} + +@article {Chinburg1994, + AUTHOR = {Chinburg, T.}, + TITLE = {Galois structure of de {R}ham cohomology of tame covers of + schemes}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {139}, + YEAR = {1994}, + NUMBER = {2}, + PAGES = {443--490}, + ISSN = {0003-486X}, + MRCLASS = {11R33 (14F40 14G10)}, + MRNUMBER = {1274097}, +MRREVIEWER = {Boas Erez}, + DOI = {10.2307/2946586}, + URL = {https://doi.org/10.2307/2946586}, +} + +@article {Kock2004, + AUTHOR = {K\"{o}ck, B.}, + TITLE = {Galois structure of {Z}ariski cohomology for weakly ramified + covers of curves}, + JOURNAL = {Amer. J. Math.}, + FJOURNAL = {American Journal of Mathematics}, + VOLUME = {126}, + YEAR = {2004}, + NUMBER = {5}, + PAGES = {1085--1107}, + ISSN = {0002-9327}, + MRCLASS = {11R33 (11G30 14H30)}, + MRNUMBER = {2089083}, +MRREVIEWER = {Nigel Byott}, + URL = + {http://muse.jhu.edu/journals/american_journal_of_mathematics/v126/126.5k"ock.pdf}, +} + +@article {DeligneIllusie_relevements, + AUTHOR = {Deligne, P. and Illusie, L.}, + TITLE = {Rel\`evements modulo {$p^2$} et d\'{e}composition du complexe de de + {R}ham}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {89}, + YEAR = {1987}, + NUMBER = {2}, + PAGES = {247--270}, + ISSN = {0020-9910}, + MRCLASS = {14F40 (14C30)}, + MRNUMBER = {894379}, +MRREVIEWER = {Thomas Zink}, + DOI = {10.1007/BF01389078}, + URL = {https://doi.org/10.1007/BF01389078}, +} + +@article {PriesZhu_p_rank_AS, + AUTHOR = {Pries, R. and Zhu, H. J.}, + TITLE = {The {$p$}-rank stratification of {A}rtin-{S}chreier curves}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {62}, + YEAR = {2012}, + NUMBER = {2}, + PAGES = {707--726}, + ISSN = {0373-0956}, + MRCLASS = {11G15 (14H10)}, + MRNUMBER = {2985514}, +MRREVIEWER = {Eric Errthum}, + DOI = {10.5802/aif.2692}, + URL = {https://doi.org/10.5802/aif.2692}, +} + +@book {Jacobson_basic_I, + AUTHOR = {Jacobson, N.}, + TITLE = {Basic algebra. {I}}, + EDITION = {Second}, + PUBLISHER = {W. H. Freeman and Company, New York}, + YEAR = {1985}, + PAGES = {xviii+499}, + ISBN = {0-7167-1480-9}, + MRCLASS = {00A05 (12-01)}, + MRNUMBER = {780184}, +} + +@article {Subrao_p_rank, + AUTHOR = {Subrao, D.}, + TITLE = {The {$p$}-rank of {A}rtin-{S}chreier curves}, + JOURNAL = {Manuscripta Math.}, + FJOURNAL = {Manuscripta Mathematica}, + VOLUME = {16}, + YEAR = {1975}, + NUMBER = {2}, + PAGES = {169--193}, + ISSN = {0025-2611}, + MRCLASS = {14H45 (14H30)}, + MRNUMBER = {0376693}, +MRREVIEWER = {K. Kiyek}, + DOI = {10.1007/BF01181639}, + URL = {https://doi.org/10.1007/BF01181639}, +} + +@article {GrothendieckQuelques, + AUTHOR = {Grothendieck, A.}, + TITLE = {Sur quelques points d'alg\`ebre homologique}, + JOURNAL = {T\^{o}hoku Math. J. (2)}, + FJOURNAL = {The Tohoku Mathematical Journal. Second Series}, + VOLUME = {9}, + YEAR = {1957}, + PAGES = {119--221}, + ISSN = {0040-8735}, + MRCLASS = {18.00}, + MRNUMBER = {0102537}, +MRREVIEWER = {D. Buchsbaum}, + DOI = {10.2748/tmj/1178244839}, + URL = {https://doi.org/10.2748/tmj/1178244839}, +} + +@incollection {WedhornDeRham, + AUTHOR = {Wedhorn, T.}, + TITLE = {De {R}ham cohomology of varieties over fields of positive + characteristic}, + BOOKTITLE = {Higher-dimensional geometry over finite fields}, + SERIES = {NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur.}, + VOLUME = {16}, + PAGES = {269--314}, + PUBLISHER = {IOS, Amsterdam}, + YEAR = {2008}, + MRCLASS = {14F40 (14J28)}, + MRNUMBER = {2484083}, +} + +@article {HartshorneDeRham, + AUTHOR = {Hartshorne, R.}, + TITLE = {On the {D}e {R}ham cohomology of algebraic varieties}, + JOURNAL = {Inst. Hautes \'{E}tudes Sci. Publ. Math.}, + FJOURNAL = {Institut des Hautes \'{E}tudes Scientifiques. Publications + Math\'{e}matiques}, + NUMBER = {45}, + YEAR = {1975}, + PAGES = {5--99}, + ISSN = {0073-8301}, + MRCLASS = {14F20}, + MRNUMBER = {0432647}, +MRREVIEWER = {D. Lieberman}, + URL = {http://www.numdam.org/item?id=PMIHES_1975__45__5_0}, +} + +@book {Weibel, + AUTHOR = {Weibel, Ch. A.}, + TITLE = {An introduction to homological algebra}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {38}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {1994}, + PAGES = {xiv+450}, + ISBN = {0-521-43500-5; 0-521-55987-1}, + MRCLASS = {18-01 (16-01 17-01 20-01 55Uxx)}, + MRNUMBER = {1269324}, +MRREVIEWER = {Kenneth A. Brown}, + DOI = {10.1017/CBO9781139644136}, + URL = {http://dx.doi.org/10.1017/CBO9781139644136}, +} + +@article {BertinMezard2000, + AUTHOR = {Bertin, J. and M\'{e}zard, A.}, + TITLE = {D\'{e}formations formelles des rev\^{e}tements sauvagement ramifi\'{e}s de + courbes alg\'{e}briques}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {141}, + YEAR = {2000}, + NUMBER = {1}, + PAGES = {195--238}, + ISSN = {0020-9910}, + MRCLASS = {14D15 (14D20 14H10 14H30 14H37)}, + MRNUMBER = {1767273}, +MRREVIEWER = {Akio Tamagawa}, + DOI = {10.1007/s002220000071}, + URL = {https://doi.org/10.1007/s002220000071}, +} + +@article {Kontogeorgis, + AUTHOR = {Kontogeorgis, A.}, + TITLE = {On the tangent space of the deformation functor of curves with + automorphisms}, + JOURNAL = {Algebra Number Theory}, + FJOURNAL = {Algebra \& Number Theory}, + VOLUME = {1}, + YEAR = {2007}, + NUMBER = {2}, + PAGES = {119--161}, + ISSN = {1937-0652}, + MRCLASS = {14H37 (14B10 14D15)}, + MRNUMBER = {2361938}, +MRREVIEWER = {Arvid Siqveland}, + DOI = {10.2140/ant.2007.1.119}, + URL = {https://doi.org/10.2140/ant.2007.1.119}, +} + +@book {HallLie, + AUTHOR = {Hall, B.}, + TITLE = {Lie groups, {L}ie algebras, and representations}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {222}, + EDITION = {Second}, + NOTE = {An elementary introduction}, + PUBLISHER = {Springer, Cham}, + YEAR = {2015}, + PAGES = {xiv+449}, + ISBN = {978-3-319-13466-6; 978-3-319-13467-3}, + MRCLASS = {22-01 (17-01)}, + MRNUMBER = {3331229}, + DOI = {10.1007/978-3-319-13467-3}, + URL = {https://doi.org/10.1007/978-3-319-13467-3}, +} + +@book {ErdmannWildon, + AUTHOR = {Erdmann, K. and Wildon, M. J.}, + TITLE = {Introduction to {L}ie algebras}, + SERIES = {Springer Undergraduate Mathematics Series}, + PUBLISHER = {Springer-Verlag London, Ltd., London}, + YEAR = {2006}, + PAGES = {x+251}, + ISBN = {978-1-84628-040-5; 1-84628-040-0}, + MRCLASS = {17B05 (17-01 17B20)}, + MRNUMBER = {2218355}, +MRREVIEWER = {Aloysius Helminck}, + DOI = {10.1007/1-84628-490-2}, + URL = {https://doi.org/10.1007/1-84628-490-2}, +} + +@book {JacobsonLie, + AUTHOR = {Jacobson, N.}, + TITLE = {Lie algebras}, + NOTE = {Republication of the 1962 original}, + PUBLISHER = {Dover Publications, Inc., New York}, + YEAR = {1979}, + PAGES = {ix+331}, + ISBN = {0-486-63832-4}, + MRCLASS = {17-01}, + MRNUMBER = {559927}, +} + +@book {HumphreysLie, + AUTHOR = {Humphreys, J. E.}, + TITLE = {Introduction to {L}ie algebras and representation theory}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {9}, + NOTE = {Second printing, revised}, + PUBLISHER = {Springer-Verlag, New York-Berlin}, + YEAR = {1978}, + PAGES = {xii+171}, + ISBN = {0-387-90053-5}, + MRCLASS = {17Bxx}, + MRNUMBER = {499562}, +MRREVIEWER = {I. P. Shestakov}, +} + +@book {Kirillov, + AUTHOR = {Kirillov, A.}, + TITLE = {An introduction to {L}ie groups and {L}ie algebras}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {113}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2008}, + PAGES = {xii+222}, + ISBN = {978-0-521-88969-8}, + MRCLASS = {22-01 (17-01 17Bxx 22Exx)}, + MRNUMBER = {2440737}, +MRREVIEWER = {Erik Koelink}, + DOI = {10.1017/CBO9780511755156}, + URL = {https://doi.org/10.1017/CBO9780511755156}, +} + +@article {Hall2008, + AUTHOR = {Hall, Ch.}, + TITLE = {Big symplectic or orthogonal monodromy modulo {$l$}}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {141}, + YEAR = {2008}, + NUMBER = {1}, + PAGES = {179--203}, + ISSN = {0012-7094}, + MRCLASS = {11G05 (11G10 12F12 14D05 14K15)}, + MRNUMBER = {2372151}, +MRREVIEWER = {Jeffrey D. Achter}, + DOI = {10.1215/S0012-7094-08-14115-8}, + URL = {https://doi.org/10.1215/S0012-7094-08-14115-8}, +} + + +@article {Hall2011, + AUTHOR = {Hall, Ch.}, + TITLE = {An open-image theorem for a general class of abelian + varieties}, + NOTE = {With an appendix by Emmanuel Kowalski}, + JOURNAL = {Bull. Lond. Math. Soc.}, + FJOURNAL = {Bulletin of the London Mathematical Society}, + VOLUME = {43}, + YEAR = {2011}, + NUMBER = {4}, + PAGES = {703--711}, + ISSN = {0024-6093}, + MRCLASS = {11G10 (14K15)}, + MRNUMBER = {2820155}, +MRREVIEWER = {Ivica Gusi\'{c}}, + DOI = {10.1112/blms/bdr004}, + URL = {https://doi.org/10.1112/blms/bdr004}, +} + +@article {Garnek2018, + AUTHOR = {Garnek, J.}, + TITLE = {On {$p$}-degree of elliptic curves}, + JOURNAL = {Int. J. Number Theory}, + FJOURNAL = {International Journal of Number Theory}, + VOLUME = {14}, + YEAR = {2018}, + NUMBER = {3}, + PAGES = {693--704}, + ISSN = {1793-0421}, + MRCLASS = {11G07 (11G05)}, + MRNUMBER = {3786643}, + DOI = {10.1142/S1793042118500434}, + URL = {https://doi.org/10.1142/S1793042118500434}, +} + +@incollection {Greenberg2001, + AUTHOR = {Greenberg, R.}, + TITLE = {Iwasawa theory---past and present}, + BOOKTITLE = {Class field theory---its centenary and prospect ({T}okyo, + 1998)}, + SERIES = {Adv. Stud. Pure Math.}, + VOLUME = {30}, + PAGES = {335--385}, + PUBLISHER = {Math. Soc. Japan, Tokyo}, + YEAR = {2001}, + MRCLASS = {11R23 (11-02)}, + MRNUMBER = {1846466}, +MRREVIEWER = {Yuichiro Taguchi}, +} + +@book {MumfordAV, + AUTHOR = {Mumford, D.}, + TITLE = {Abelian varieties}, + SERIES = {Tata Institute of Fundamental Research Studies in Mathematics}, + VOLUME = {5}, + NOTE = {With appendices by C. P. Ramanujam and Yuri Manin, + Corrected reprint of the second (1974) edition}, + PUBLISHER = {Published for the Tata Institute of Fundamental Research, + Bombay; by Hindustan Book Agency, New Delhi}, + YEAR = {2008}, + PAGES = {xii+263}, + ISBN = {978-81-85931-86-9; 81-85931-86-0}, + MRCLASS = {14Kxx}, + MRNUMBER = {2514037}, +} + +@article{GrossHarris1981, +author = {Gross, B. H. and Harris, J.}, +journal = {Annales scientifiques de l'\'{E}cole Normale Sup\'{e}rieure}, +keywords = {real theta-characteristics; real abelian varieties; complex conjugation on complex algebraic curves; real curves; Picard scheme; Real hyperelliptic curves; real plane curves; real trigonal curves; real moduli}, +language = {eng}, +number = {2}, +pages = {157-182}, +publisher = {Elsevier}, +title = {Real algebraic curves}, +url = {http://eudml.org/doc/82070}, +volume = {14}, +year = {1981}, +} + +@book {Serre1992, + AUTHOR = {Serre, J.-P.}, + TITLE = {Lie algebras and {L}ie groups}, + SERIES = {Lecture Notes in Mathematics}, + VOLUME = {1500}, + EDITION = {Second}, + NOTE = {1964 lectures given at Harvard University}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1992}, + PAGES = {viii+168}, + ISBN = {3-540-55008-9}, + MRCLASS = {17-01 (17Bxx 22-01)}, + MRNUMBER = {1176100}, +} + +@book {Serre1989, + AUTHOR = {Serre, J.-P.}, + TITLE = {Abelian {$l$}-adic representations and elliptic curves}, + SERIES = {Advanced Book Classics}, + EDITION = {Second}, + NOTE = {With the collaboration of Willem Kuyk and John Labute}, + PUBLISHER = {Addison-Wesley Publishing Company, Advanced Book Program, + Redwood City, CA}, + YEAR = {1989}, + PAGES = {xxiv+184}, + ISBN = {0-201-09384-7}, + MRCLASS = {11G05 (11F33 11F80)}, + MRNUMBER = {1043865}, +} + +@article{SY2016, + author = {{Sairaiji}, F. and {Yamauchi}, T.}, + title = "{On the class numbers of the fields of the $p^n$-torsion points of elliptic curves over $\mathbb{Q}$}", + journal = {ArXiv e-prints}, +archivePrefix = "arXiv", + eprint = {1603.01296}, + primaryClass = "math.NT", + keywords = {Mathematics - Number Theory}, + year = 2016, + month = mar, + adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160301296S}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + +@article {Ribet1979, + AUTHOR = {Ribet, K. A.}, + TITLE = {Kummer theory on extensions of abelian varieties by tori}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {46}, + YEAR = {1979}, + NUMBER = {4}, + PAGES = {745--761}, + ISSN = {0012-7094}, + MRCLASS = {14K15 (12A35 12F10)}, + MRNUMBER = {552524}, +MRREVIEWER = {Daniel Coray}, + URL = {http://projecteuclid.org/euclid.dmj/1077313720}, +} + +@Inbook{Ogus1981, +author="Ogus, A.", +title="Hodge Cycles and Crystalline Cohomology", +bookTitle="Hodge Cycles, Motives, and Shimura Varieties", +year="1981", +publisher="Springer Berlin Heidelberg", +address="Berlin, Heidelberg", +pages="357--414", +abstract="This paper is a collection of musings about several questions related to crystalline cohomology that have plagued me for the past few years. It contains many more conjectures than proofs, and my justification for publishing is the hope that others will find the problems as intriguing as I did but perhaps have more success in solving them.", +isbn="978-3-540-38955-2", +doi="10.1007/978-3-540-38955-2_8", +url="https://doi.org/10.1007/978-3-540-38955-2_8" +} + + +@article {Dieulefait2002, + AUTHOR = {Dieulefait, L. V.}, + TITLE = {Explicit determination of the images of the {G}alois + representations attached to abelian surfaces with {${\rm + End}(A)=\Bbb Z$}}, + JOURNAL = {Experiment. Math.}, + FJOURNAL = {Experimental Mathematics}, + VOLUME = {11}, + YEAR = {2002}, + NUMBER = {4}, + PAGES = {503--512 (2003)}, + ISSN = {1058-6458}, + MRCLASS = {11F80 (11G10)}, + MRNUMBER = {1969642}, +MRREVIEWER = {Thomas A. Weston}, + URL = {http://projecteuclid.org/euclid.em/1057864660}, +} + +@article {ClarkLacy2016, +AUTHOR = {Clark, P. L. and Lacy, A.}, +TITLE = {There are genus one curves of every index over every infinite, +finitely generated field}, +JOURNAL = {J. Reine Angew. Math.}, +FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's +Journal]}, +VOLUME = {749}, +YEAR = {2019}, +PAGES = {65--86}, +ISSN = {0075-4102}, +MRCLASS = {11G05 (14H25)}, +MRNUMBER = {3935899}, +MRREVIEWER = {Remke Kloosterman}, +DOI = {10.1515/crelle-2016-0037}, +URL = {https://doi.org/10.1515/crelle-2016-0037}, +} + +@book {BLR1990, + AUTHOR = {Bosch, S. and L\"utkebohmert, W. and Raynaud, M.}, + TITLE = {N\'eron models}, + SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results + in Mathematics and Related Areas (3)]}, + VOLUME = {21}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {1990}, + PAGES = {x+325}, + ISBN = {3-540-50587-3}, + MRCLASS = {14K15 (11G10 14L15)}, + MRNUMBER = {1045822}, +MRREVIEWER = {James Milne}, + DOI = {10.1007/978-3-642-51438-8}, + URL = {https://doi.org/10.1007/978-3-642-51438-8}, +} + +@article{Bashmakov, + author={M. I. Bashmakov}, + title={The Cohomology of Abelian Varieties Over a Number Field}, + journal={Russian Mathematical Surveys}, + volume={27}, + number={6}, + pages={25}, + url={http://stacks.iop.org/0036-0279/27/i=6/a=R03}, + year={1972}, +} + +@incollection {Kedlaya2008, + AUTHOR = {Kedlaya, K. S.}, + TITLE = {{$p$}-adic cohomology: from theory to practice}, + BOOKTITLE = {{$p$}-adic geometry}, + SERIES = {Univ. Lecture Ser.}, + VOLUME = {45}, + PAGES = {175--203}, + PUBLISHER = {Amer. Math. Soc., Providence, RI}, + YEAR = {2008}, + MRCLASS = {14F30 (14F40)}, + MRNUMBER = {2482348}, +MRREVIEWER = {Michel Gros}, + DOI = {10.1090/ulect/045/05}, + URL = {https://doi.org/10.1090/ulect/045/05}, +} + +@article {Kedlaya2001, + AUTHOR = {Kedlaya, K. S.}, + TITLE = {Counting points on hyperelliptic curves using + {M}onsky-{W}ashnitzer cohomology}, + JOURNAL = {J. Ramanujan Math. Soc.}, + FJOURNAL = {Journal of the Ramanujan Mathematical Society}, + VOLUME = {16}, + YEAR = {2001}, + NUMBER = {4}, + PAGES = {323--338}, + ISSN = {0970-1249}, + MRCLASS = {14G05 (11G25 14F43 14G15)}, + MRNUMBER = {1877805}, +MRREVIEWER = {Miriam D. Abd\'on}, +} + +@article {Towse1996, + AUTHOR = {Towse, Ch.}, + TITLE = {Weierstrass points on cyclic covers of the projective line}, + JOURNAL = {Trans. Amer. Math. Soc.}, + FJOURNAL = {Transactions of the American Mathematical Society}, + VOLUME = {348}, + YEAR = {1996}, + NUMBER = {8}, + PAGES = {3355--3378}, + ISSN = {0002-9947}, + MRCLASS = {14H55 (11G30 14H45)}, + MRNUMBER = {1357406}, +MRREVIEWER = {Masaaki Homma}, + DOI = {10.1090/S0002-9947-96-01649-2}, + URL = {https://doi.org/10.1090/S0002-9947-96-01649-2}, +} + +@article{MolinNeurohr2017, +author = {Molin, P. and Neurohr, Ch.}, +year = {2017}, +month = {07}, +pages = {}, +title = {Computing period matrices and the Abel-Jacobi map of superelliptic curves}, +booktitle = {Mathematics of Computation} +} + +@article {Hortsch2012, + AUTHOR = {Hortsch, R.}, + TITLE = {On the canonical representation of curves in positive + characteristic}, + JOURNAL = {New York J. Math.}, + FJOURNAL = {New York Journal of Mathematics}, + VOLUME = {18}, + YEAR = {2012}, + PAGES = {911--924}, + ISSN = {1076-9803}, + MRCLASS = {14G17 (11G05)}, + MRNUMBER = {3007205}, +MRREVIEWER = {Rachel J. Pries}, + URL = {http://nyjm.albany.edu:8000/j/2012/18_911.html}, +} + +@article {KockTait2018, + AUTHOR = {K\"ock, B. and Tait, J.}, + TITLE = {On the de-{R}ham cohomology of hyperelliptic curves}, + JOURNAL = {Res. Number Theory}, + FJOURNAL = {Research in Number Theory}, + VOLUME = {4}, + YEAR = {2018}, + NUMBER = {2}, + PAGES = {4:19}, + ISSN = {2363-9555}, + MRCLASS = {14F40 (14G17 14H37)}, + MRNUMBER = {3782449}, + DOI = {10.1007/s40993-018-0111-4}, + URL = {https://doi.org/10.1007/s40993-018-0111-4}, +} + +@article {SupZal, + author = {Supunenko, I.~D. and Zalesskii, A.~E.}, + title = {Reduced symmetric powers of natural realizations of + the groups $SL_m(P)$ and $Sp_m(P)$ and their restrictions to subgroups}, + journal = {Siberian Math. J.}, + volume = {31}, + number = {4}, + pages = {33--46} +} + +@article {Sosnovskii, + AUTHOR = {Sosnovski\u\i , Ju. V.}, + TITLE = {Commutator structure of symplectic groups}, + JOURNAL = {Mat. Zametki}, + FJOURNAL = {Akademiya Nauk Soyuza SSR. Matematicheskie Zametki}, + VOLUME = {24}, + YEAR = {1978}, + NUMBER = {5}, + PAGES = {641--648, 734}, + ISSN = {0025-567X}, + MRCLASS = {20G30}, + MRNUMBER = {517424}, +MRREVIEWER = {E. Vinberg}, +} + +@book {SerreOeurvesIV, + AUTHOR = {Serre, J.-P.}, + TITLE = {Oeuvres/{C}ollected papers. {IV}. 1985--1998}, + SERIES = {Springer Collected Works in Mathematics}, + NOTE = {Reprint of the 2000 edition}, + PUBLISHER = {Springer, Heidelberg}, + YEAR = {2013}, + PAGES = {viii+694}, + ISBN = {978-3-642-39839-1}, + MRCLASS = {01A75 (01A70)} +} + +@article {Neron1952, + AUTHOR = {N\'eron, A.}, + TITLE = {Probl\`emes arithm\'etiques et g\'eom\'etriques rattach\'es \`a la notion + de rang d'une courbe alg\'ebrique dans un corps}, + JOURNAL = {Bull. Soc. Math. France}, + FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France}, + VOLUME = {80}, + YEAR = {1952}, + PAGES = {101--166}, + ISSN = {0037-9484}, + MRCLASS = {14.0X}, + MRNUMBER = {0056951}, +MRREVIEWER = {B. Segre}, + URL = {http://www.numdam.org/item?id=BSMF_1952__80__101_0}, +} + +@book {Marcus1977, + AUTHOR = {Marcus, D. A.}, + TITLE = {Number fields}, + NOTE = {Universitext}, + PUBLISHER = {Springer-Verlag, New York-Heidelberg}, + YEAR = {1977}, + PAGES = {viii+279}, + ISBN = {0-387-90279-1}, + MRCLASS = {12-01}, + MRNUMBER = {0457396}, +MRREVIEWER = {Ezra Brown}, +} + +@article {Moonen2004, + AUTHOR = {Moonen, B.}, + TITLE = {Serre-{T}ate theory for moduli spaces of {PEL} type}, + JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)}, + FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme + S\'erie}, + VOLUME = {37}, + YEAR = {2004}, + NUMBER = {2}, + PAGES = {223--269}, + ISSN = {0012-9593}, + MRCLASS = {11G18 (14G35)}, + MRNUMBER = {2061781}, +MRREVIEWER = {Ulrich G\"ortz}, + URL = {https://doi.org/10.1016/j.ansens.2003.04.004}, +} + +@article {Breuer2002, + AUTHOR = {Breuer, F.}, + TITLE = {Distinguished liftings and the {A}ndr\'e-{O}ort conjecture}, + JOURNAL = {Quaest. Math.}, + FJOURNAL = {Quaestiones Mathematicae. Journal of the South African + Mathematical Society}, + VOLUME = {25}, + YEAR = {2002}, + NUMBER = {3}, + PAGES = {363--380}, + ISSN = {1607-3606}, + MRCLASS = {11G15 (11G35 14G35)}, + MRNUMBER = {1931287}, +MRREVIEWER = {James Milne}, + URL = {https://doi.org/10.2989/16073600209486023}, +} + +@incollection {BrokerStevenHagen2004, + AUTHOR = {Br\"oker, R. and Stevenhagen, P.}, + TITLE = {Elliptic curves with a given number of points}, + BOOKTITLE = {Algorithmic number theory}, + SERIES = {Lecture Notes in Comput. Sci.}, + VOLUME = {3076}, + PAGES = {117--131}, + PUBLISHER = {Springer, Berlin}, + YEAR = {2004}, + MRCLASS = {11G20}, + MRNUMBER = {2137348}, +MRREVIEWER = {Christian Wittmann}, + URL = {https://doi.org/10.1007/978-3-540-24847-7_8}, +} + +@article {AGP2013, + AUTHOR = {Arias-de-Reyna, S. and Gajda, W. and Petersen, + S.}, + TITLE = {Big monodromy theorem for abelian varieties over finitely + generated fields}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {217}, + YEAR = {2013}, + NUMBER = {2}, + PAGES = {218--229}, + ISSN = {0022-4049}, + MRCLASS = {14K15 (11G10 11G30)}, + MRNUMBER = {2969246}, +MRREVIEWER = {John T. Cullinan}, + URL = {https://doi.org/10.1016/j.jpaa.2012.06.010}, +} + +@article {FKY2007, + AUTHOR = {Fukuda, T. and Komatsu, K. and Yamagata, Sh.}, + TITLE = {Iwasawa {$\lambda$}-invariants and {M}ordell-{W}eil ranks of + abelian varieties with complex multiplication}, + JOURNAL = {Acta Arith.}, + FJOURNAL = {Acta Arithmetica}, + VOLUME = {127}, + YEAR = {2007}, + NUMBER = {4}, + PAGES = {305--307}, + ISSN = {0065-1036}, + MRCLASS = {11G15 (11G10 11R23)}, + MRNUMBER = {2302046}, +MRREVIEWER = {Hui June Zhu}, + URL = {https://doi.org/10.4064/aa127-4-1}, +} + +@article{Mordell1922, +author="Mordell, L. J.", +title="On the rational resolutions of the indeterminate equations of the third and fourth degree", +journal="Proc. Cambridge Phil. Soc.", +ISSN="", +publisher="", +year="1922", +month="", +volume="21", +number="", +pages="179-192", +URL="http://ci.nii.ac.jp/naid/10014601152/en/", +DOI="", +} + +@article {Elkies1987, + AUTHOR = {Elkies, N. D.}, + TITLE = {The existence of infinitely many supersingular primes for + every elliptic curve over {${\bf Q}$}}, + JOURNAL = {Invent. Math.}, + FJOURNAL = {Inventiones Mathematicae}, + VOLUME = {89}, + YEAR = {1987}, + NUMBER = {3}, + PAGES = {561--567}, + ISSN = {0020-9910}, + MRCLASS = {11G05 (14G25)}, + MRNUMBER = {903384}, +MRREVIEWER = {David Grant}, + URL = {https://doi.org/10.1007/BF01388985}, +} + +@article {Berbec2009, + AUTHOR = {Berbec, I.}, + TITLE = {Group schemes over {A}rtinian rings and applications}, + JOURNAL = {Ann. Inst. Fourier (Grenoble)}, + FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier}, + VOLUME = {59}, + YEAR = {2009}, + NUMBER = {6}, + PAGES = {2371--2427}, + ISSN = {0373-0956}, + MRCLASS = {14L15 (14L05)}, + MRNUMBER = {2640924}, +MRREVIEWER = {Alan Koch}, + URL = {http://aif.cedram.org/item?id=AIF_2009__59_6_2371_0}, +} + +@article {DworkOgus1986, + AUTHOR = {Dwork, B. and Ogus, A.}, + TITLE = {Canonical liftings of {J}acobians}, + JOURNAL = {Compositio Math.}, + FJOURNAL = {Compositio Mathematica}, + VOLUME = {58}, + YEAR = {1986}, + NUMBER = {1}, + PAGES = {111--131}, + ISSN = {0010-437X}, + MRCLASS = {14H10 (11G10 14H40)}, + MRNUMBER = {834049}, +MRREVIEWER = {Tsutomu Sekiguchi}, + URL = {http://www.numdam.org/item?id=CM_1986__58_1_111_0}, +} + +@incollection {GHKRW2006, + AUTHOR = {Gaudry, P. and Houtmann, T. and Kohel, D. and Ritzenthaler, C. + and Weng, A.}, + TITLE = {The 2-adic {CM} method for genus 2 curves with application to + cryptography}, + BOOKTITLE = {Advances in cryptology---{ASIACRYPT} 2006}, + SERIES = {Lecture Notes in Comput. Sci.}, + VOLUME = {4284}, + PAGES = {114--129}, + PUBLISHER = {Springer, Berlin}, + YEAR = {2006}, + MRCLASS = {94A60 (11T71)}, + MRNUMBER = {2444631}, + URL = {https://doi.org/10.1007/11935230_8}, +} + +@article {CRKL2008, + AUTHOR = {Carls, R. and Kohel, D. and Lubicz, D.}, + TITLE = {Higher-dimensional 3-adic {CM} construction}, + JOURNAL = {J. Algebra}, + FJOURNAL = {Journal of Algebra}, + VOLUME = {319}, + YEAR = {2008}, + NUMBER = {3}, + PAGES = {971--1006}, + ISSN = {0021-8693}, + MRCLASS = {14K25}, + MRNUMBER = {2379090}, + URL = {https://doi.org/10.1016/j.jalgebra.2007.11.016}, +} + +@incollection {GHKRW2006, + AUTHOR = {Gaudry, P. and Houtmann, T. and Kohel, D. and Ritzenthaler, C. + and Weng, A.}, + TITLE = {The 2-adic {CM} method for genus 2 curves with application to + cryptography}, + BOOKTITLE = {Advances in cryptology---{ASIACRYPT} 2006}, + SERIES = {Lecture Notes in Comput. Sci.}, + VOLUME = {4284}, + PAGES = {114--129}, + PUBLISHER = {Springer, Berlin}, + YEAR = {2006}, + MRCLASS = {94A60 (11T71)}, + MRNUMBER = {2444631}, + URL = {https://doi.org/10.1007/11935230_8}, +} + +@incollection {BBEL2008, + AUTHOR = {Belding, Juliana and Br\"oker, Reinier and Enge, Andreas and + Lauter, Kristin}, + TITLE = {Computing {H}ilbert class polynomials}, + BOOKTITLE = {Algorithmic number theory}, + SERIES = {Lecture Notes in Comput. Sci.}, + VOLUME = {5011}, + PAGES = {282--295}, + PUBLISHER = {Springer, Berlin}, + YEAR = {2008}, + MRCLASS = {11Y40 (11C08 11R54)}, + MRNUMBER = {2467854}, +MRREVIEWER = {Horst Brunotte}, + URL = {https://doi.org/10.1007/978-3-540-79456-1_19}, +} + +@incollection {Kohel2008, + AUTHOR = {Kohel, D. R.}, + TITLE = {Complex multiplication and canonical lifts}, + BOOKTITLE = {Algebraic geometry and its applications}, + SERIES = {Ser. Number Theory Appl.}, + VOLUME = {5}, + PAGES = {67--83}, + PUBLISHER = {World Sci. Publ., Hackensack, NJ}, + YEAR = {2008}, + MRCLASS = {14K22 (14K15)}, + MRNUMBER = {2484048}, +MRREVIEWER = {Damian R\"ossler}, + URL = {https://doi.org/10.1142/9789812793430_0003}, +} + +@article {SatohSkjernaaTaguchi2003, + AUTHOR = {Satoh, Takakazu and Skjernaa, Berit and Taguchi, Yuichiro}, + TITLE = {Fast computation of canonical lifts of elliptic curves and its + application to point counting}, + JOURNAL = {Finite Fields Appl.}, + FJOURNAL = {Finite Fields and their Applications}, + VOLUME = {9}, + YEAR = {2003}, + NUMBER = {1}, + PAGES = {89--101}, + ISSN = {1071-5797}, + MRCLASS = {14G50 (11G20 11T71 94A60)}, + MRNUMBER = {1954785}, +MRREVIEWER = {J. W. P. Hirschfeld}, + URL = {https://doi.org/10.1016/S1071-5797(02)00013-8}, +} + +@article {OortSekiguchi1986, + AUTHOR = {Oort, F. and Sekiguchi, T.}, + TITLE = {The canonical lifting of an ordinary {J}acobian variety need + not be a {J}acobian variety}, + JOURNAL = {J. Math. Soc. Japan}, + FJOURNAL = {Journal of the Mathematical Society of Japan}, + VOLUME = {38}, + YEAR = {1986}, + NUMBER = {3}, + PAGES = {427--437}, + ISSN = {0025-5645}, + MRCLASS = {14K10 (14H40)}, + MRNUMBER = {845711}, +MRREVIEWER = {Ryuji Sasaki}, + URL = {https://doi.org/10.2969/jmsj/03830427}, +} + +@article {Erdogan2015, + AUTHOR = {Erdo{\u g}an, Altan}, + TITLE = {A universal formula for the {$j$}-invariant of the canonical + lifting}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {150}, + YEAR = {2015}, + PAGES = {26--40}, + ISSN = {0022-314X}, + MRCLASS = {11G07 (14K05)}, + MRNUMBER = {3304604}, +MRREVIEWER = {Jeroen Sijsling}, + URL = {https://doi.org/10.1016/j.jnt.2014.11.002}, +} + +@article {Finotti2012, + AUTHOR = {Finotti, Lu\'\i s R. A.}, + TITLE = {Nonexistence of pseudo-canonical liftings}, + JOURNAL = {Int. J. Number Theory}, + FJOURNAL = {International Journal of Number Theory}, + VOLUME = {8}, + YEAR = {2012}, + NUMBER = {1}, + PAGES = {31--51}, + ISSN = {1793-0421}, + MRCLASS = {11G07 (13F35)}, + MRNUMBER = {2887881}, +MRREVIEWER = {Markus Szymik}, + URL = {https://doi.org/10.1142/S1793042112500029}, +} + +@article {Finotti2011, + AUTHOR = {Finotti, Lu\'\i s R. A.}, + TITLE = {Computations with {W}itt vectors of length 3}, + JOURNAL = {J. Th\'eor. Nombres Bordeaux}, + FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux}, + VOLUME = {23}, + YEAR = {2011}, + NUMBER = {2}, + PAGES = {417--454}, + ISSN = {1246-7405}, + MRCLASS = {13F35}, + MRNUMBER = {2817938}, +MRREVIEWER = {Markus Szymik}, + URL = {http://jtnb.cedram.org/item?id=JTNB_2011__23_2_417_0}, +} + +@article {Finotti2010, + AUTHOR = {Finotti, Lu\'\i s R. A.}, + TITLE = {Lifting the {$j$}-invariant: questions of {M}azur and {T}ate}, + JOURNAL = {J. Number Theory}, + FJOURNAL = {Journal of Number Theory}, + VOLUME = {130}, + YEAR = {2010}, + NUMBER = {3}, + PAGES = {620--638}, + ISSN = {0022-314X}, + MRCLASS = {11G20}, + MRNUMBER = {2584845}, +MRREVIEWER = {Niko Naumann}, + URL = {https://doi.org/10.1016/j.jnt.2009.10.009}, +} + +@article {Mazur1997, + AUTHOR = {Mazur, B.}, + TITLE = {An "infinite fern" in the universal deformation space of + {G}alois representations}, + NOTE = {Journ\'ees Arithm\'etiques (Barcelona, 1995)}, + JOURNAL = {Collect. Math.}, + FJOURNAL = {Universitat de Barcelona. Collectanea Mathematica}, + VOLUME = {48}, + YEAR = {1997}, + NUMBER = {1-2}, + PAGES = {155--193}, + ISSN = {0010-0757}, + MRCLASS = {11F33 (11F80)}, + MRNUMBER = {1464022}, +MRREVIEWER = {Andrea Mori}, +} + +@article {Larsen1995, + AUTHOR = {Larsen, M.}, + TITLE = {Maximality of {G}alois actions for compatible systems}, + JOURNAL = {Duke Math. J.}, + FJOURNAL = {Duke Mathematical Journal}, + VOLUME = {80}, + YEAR = {1995}, + NUMBER = {3}, + PAGES = {601--630}, + ISSN = {0012-7094}, + MRCLASS = {11G09 (11G10 11S37 20G25)}, + MRNUMBER = {1370110}, +MRREVIEWER = {Ernst-Wilhelm Zink}, + URL = {https://doi.org/10.1215/S0012-7094-95-08021-1}, +} + +@article {GajdaPetersenReyna2013, + AUTHOR = {Arias-de-Reyna, Sara and Gajda, Wojciech and Petersen, + Sebastian}, + TITLE = {Big monodromy theorem for abelian varieties over finitely + generated fields}, + JOURNAL = {J. Pure Appl. Algebra}, + FJOURNAL = {Journal of Pure and Applied Algebra}, + VOLUME = {217}, + YEAR = {2013}, + NUMBER = {2}, + PAGES = {218--229}, + ISSN = {0022-4049}, + MRCLASS = {14K15 (11G10 11G30)}, + MRNUMBER = {2969246}, +MRREVIEWER = {John T. Cullinan}, + URL = {https://doi.org/10.1016/j.jpaa.2012.06.010}, +} + +@article {Mattuck1955, + AUTHOR = {Mattuck, Arthur}, + TITLE = {Abelian varieties over {$p$}-adic ground fields}, + JOURNAL = {Ann. of Math. (2)}, + FJOURNAL = {Annals of Mathematics. Second Series}, + VOLUME = {62}, + YEAR = {1955}, + PAGES = {92--119}, + ISSN = {0003-486X}, + MRCLASS = {14.0X}, + MRNUMBER = {0071116}, +MRREVIEWER = {C. Chevalley}, + URL = {https://doi.org/10.2307/2007101}, +} + +@misc{lmfdb, + shorthand = {LMFDB}, + author = {The {LMFDB Collaboration}}, + title = {The L-functions and Modular Forms Database}, + howpublished = {\url{http://www.lmfdb.org}}, + year = {2017}, + note = {[Online; accessed 12 November 2017]}, +} + +@book{Corvaja2016, + title={Integral Points on Algebraic Varieties: An Introduction to Diophantine Geometry}, + author={Corvaja, P.}, + isbn={9789380250830}, + series={Hindustan Book Agency Series}, + url={https://books.google.pl/books?id=8mnLjwEACAAJ}, + year={2016}, + publisher={Hindustan Book Agency} +} + +@book {Serre1997, + AUTHOR = {Serre, Jean-Pierre}, + TITLE = {Lectures on the {M}ordell-{W}eil theorem}, + SERIES = {Aspects of Mathematics}, + EDITION = {Third}, + NOTE = {Translated from the French and edited by Martin Brown from + notes by Michel Waldschmidt, + With a foreword by Brown and Serre}, + PUBLISHER = {Friedr. Vieweg \& Sohn, Braunschweig}, + YEAR = {1997}, + PAGES = {x+218}, + ISBN = {3-528-28968-6}, + MRCLASS = {11G10 (11D41 11G30 14G25)}, + MRNUMBER = {1757192}, + URL = {https://doi.org/10.1007/978-3-663-10632-6}, +} + +@book {Serre2008, + AUTHOR = {Serre, Jean-Pierre}, + TITLE = {Topics in {G}alois theory}, + SERIES = {Research Notes in Mathematics}, + VOLUME = {1}, + EDITION = {Second}, + NOTE = {With notes by Henri Darmon}, + PUBLISHER = {A K Peters, Ltd., Wellesley, MA}, + YEAR = {2008}, + PAGES = {xvi+120}, + ISBN = {978-1-56881-412-4}, + MRCLASS = {12F12}, + MRNUMBER = {2363329}, +} + + +@book {DummitFoote2004, + AUTHOR = {Dummit, D. S. and Foote, R. M.}, + TITLE = {Abstract algebra}, + EDITION = {Third}, + PUBLISHER = {John Wiley \& Sons, Inc., Hoboken, NJ}, + YEAR = {2004}, + PAGES = {xii+932}, + ISBN = {0-471-43334-9}, + MRCLASS = {00-01 (16-01 20-01)}, + MRNUMBER = {2286236}, +} + +@book {GelfandManin2003, + AUTHOR = {Gelfand, S. I. and Manin, Y. I.}, + TITLE = {Methods of homological algebra}, + SERIES = {Springer Monographs in Mathematics}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, Berlin}, + YEAR = {2003}, + PAGES = {xx+372}, + ISBN = {3-540-43583-2}, + MRCLASS = {18-02 (18Exx 18Gxx 55U35)}, + MRNUMBER = {1950475}, + DOI = {10.1007/978-3-662-12492-5}, + URL = {http://dx.doi.org/10.1007/978-3-662-12492-5}, +} + + +@book {Rotman2009, + AUTHOR = {Rotman, J. J.}, + TITLE = {An introduction to homological algebra}, + SERIES = {Universitext}, + EDITION = {Second}, + PUBLISHER = {Springer, New York}, + YEAR = {2009}, + PAGES = {xiv+709}, + ISBN = {978-0-387-24527-0}, + MRCLASS = {18Gxx (13Dxx 16Exx 18-01 20J06)}, + MRNUMBER = {2455920}, +MRREVIEWER = {Fernando Muro}, + DOI = {10.1007/b98977}, + URL = {http://dx.doi.org/10.1007/b98977}, +} + +@book {HiltonStammbach1997, + AUTHOR = {Hilton, P. J. and Stammbach, U.}, + TITLE = {A course in homological algebra}, + SERIES = {Graduate Texts in Mathematics}, + VOLUME = {4}, + EDITION = {Second}, + PUBLISHER = {Springer-Verlag, New York}, + YEAR = {1997}, + PAGES = {xii+364}, + ISBN = {0-387-94823-6}, + MRCLASS = {18-02 (17B56 18Gxx 20J05)}, + MRNUMBER = {1438546}, + DOI = {10.1007/978-1-4419-8566-8}, + URL = {http://dx.doi.org/10.1007/978-1-4419-8566-8}, +} + +@book {McCleary2001, + AUTHOR = {McCleary, John}, + TITLE = {A user's guide to spectral sequences}, + SERIES = {Cambridge Studies in Advanced Mathematics}, + VOLUME = {58}, + EDITION = {Second}, + PUBLISHER = {Cambridge University Press, Cambridge}, + YEAR = {2001}, + PAGES = {xvi+561}, + ISBN = {0-521-56759-9}, + MRCLASS = {55Txx (18G40)}, + MRNUMBER = {1793722}, +MRREVIEWER = {Frank Neumann}, +} + +@inbook{Tate1997, + address = "New York, NY", + author = "Tate, J.", + chapter = "Finite Flat Group Schemes", + doi = "10.1007/978-1-4612-1974-3_5", + editor = "Cornell, G. and Silverman, J. H. and Stevens, G.", + isbn = "978-1-4612-1974-3", + pages = "121--154", + publisher = "Springer New York", + title = "{Modular Forms and Fermat's Last Theorem}", + url = "http://dx.doi.org/10.1007/978-1-4612-1974-3_5", + year = "1997" +} + +@book{Silverman_AEC, + author = "Silverman, J. H.", + doi = "10.1007/978-0-387-09494-6", + edition = "Second", + isbn = "978-0-387-09493-9", + mrclass = "11-02 (11G05 11G20 14H52 14K15)", + mrnumber = "2514094", + mrreviewer = "Vasil{\cprime} {\=I}. Andr{\={\i}}{\u\i}chuk", + pages = "xx+513", + publisher = "Springer, Dordrecht", + series = "{Graduate Texts in Mathematics}", + title = "{The arithmetic of elliptic curves}", + url = "http://dx.doi.org/10.1007/978-0-387-09494-6", + volume = "106", + year = "2009" +} + +@book{Silverman_Advanced, + author = "Silverman, J. H.", + doi = "10.1007/978-1-4612-0851-8", + isbn = "0-387-94328-5", + mrclass = "11G05 (11G07 11G15 11G40 14H52)", + mrnumber = "1312368", + mrreviewer = "Henri Darmon", + pages = "xiv+525", + publisher = "Springer-Verlag, New York", + series = "{Graduate Texts in Mathematics}", + title = "{Advanced topics in the arithmetic of elliptic curves}", + url = "http://dx.doi.org/10.1007/978-1-4612-0851-8", + volume = "151", + year = "1994" +} + +@incollection{Shatz1996, + author = "Shatz, S. S.", + booktitle = "{Arithmetic geometry ({S}torrs, {C}onn., 1984)}", + mrclass = "14L05", + mrnumber = "861972", + pages = "29--78", + publisher = "Springer, New York", + title = "{Group schemes, formal groups, and {$p$}-divisible groups}", + year = "1986" +} + +@incollection{Katz1981, + author = "Katz, N. M.", + booktitle = "{Algebraic surfaces ({O}rsay, 1976--78)}", + mrclass = "14K10", + mrnumber = "638600", + mrreviewer = "William E. Lang", + pages = "138--202", + publisher = "Springer, Berlin-New York", + series = "{Lecture Notes in Math.}", + title = "{Serre-{T}ate local moduli}", + volume = "868", + year = "1981" +} + +@book{KatzMazur1985, + author = "Katz, Nicholas M. and Mazur, Barry", + isbn = "0-691-08349-5; 0-691-08352-5", + mrclass = "11G05 (11F11 14G25 14K15)", + mrnumber = "772569", + mrreviewer = "Kenneth A. Ribet", + pages = "xiv+514", + publisher = "Princeton University Press, Princeton, NJ", + series = "{Annals of Mathematics Studies}", + title = "{Arithmetic moduli of elliptic curves}", + volume = "108", + year = "1985" +} + +@book{Hartshorne1977, + author = "Hartshorne, R.", + isbn = "0-387-90244-9", + mrclass = "14-01", + mrnumber = "0463157", + mrreviewer = "Robert Speiser", + note = "Graduate Texts in Mathematics, No. 52", + pages = "xvi+496", + publisher = "Springer-Verlag, New York-Heidelberg", + title = "{Algebraic geometry}", + year = "1977" +} + +@book{IrelandRosen1990, + author = "Ireland, K. and Rosen, M.", + doi = "10.1007/978-1-4757-2103-4", + edition = "Second", + isbn = "0-387-97329-X", + mrclass = "11-01 (11-02)", + mrnumber = "1070716", + mrreviewer = "Glenn Stevens", + pages = "xiv+389", + publisher = "Springer-Verlag, New York", + series = "{Graduate Texts in Mathematics}", + title = "{A classical introduction to modern number theory}", + url = "http://dx.doi.org/10.1007/978-1-4757-2103-4", + volume = "84", + year = "1990" +} + +@article{DavidWeston2008, + author = "David, Ch. and Weston, T.", + doi = "10.4310/MRL.2008.v15.n3.a17", + fjournal = "Mathematical Research Letters", + issn = "1073-2780", + journal = "Math. Res. Lett.", + mrclass = "11G05 (11F80)", + mrnumber = "2407234", + mrreviewer = "Conjeeveram S. Rajan", + number = "3", + pages = "599--611", + title = "{Local torsion on elliptic curves and the deformation theory of {G}alois representations}", + url = "http://dx.doi.org/10.4310/MRL.2008.v15.n3.a17", + volume = "15", + year = "2008" +} + +@article{Cosgrave2014, + author = "Cosgrave, J. B. and Dilcher, K.", + doi = "10.1007/s10474-013-0357-1", + fjournal = "Acta Mathematica Hungarica", + issn = "0236-5294", + journal = "Acta Math. Hungar.", + mrclass = "11A07 (11B65)", + mrnumber = "3158860", + mrreviewer = "Tatiana Hessami Pilehrood", + number = "1", + pages = "199--230", + title = "{The {G}auss-{W}ilson theorem for quarter-intervals}", + url = "http://dx.doi.org/10.1007/s10474-013-0357-1", + volume = "142", + year = "2014" +} + +@article{Pannekoek2012, + adsnote = "Provided by the SAO/NASA Astrophysics Data System", + adsurl = "http://adsabs.harvard.edu/abs/2012arXiv1211.5833P", + archiveprefix = "arXiv", + author = "{Pannekoek}, R.", + eprint = "1211.5833", + journal = "ArXiv e-prints", + keywords = "Mathematics - Algebraic Geometry; Mathematics - Number Theory; 14H52", + month = nov, + primaryclass = "math.AG", + title = "{On p-torsion of p-adic elliptic curves with additive reduction}", + year = 2012 +} + +@book{Davenport2000, + author = "Davenport, Harold", + edition = "Third", + isbn = "0-387-95097-4", + mrclass = "11-02 (11-01 11Mxx 11Nxx)", + mrnumber = "1790423", + note = "Revised and with a preface by Hugh L. Montgomery", + pages = "xiv+177", + publisher = "Springer-Verlag, New York", + series = "{Graduate Texts in Mathematics}", + title = "{Multiplicative number theory}", + volume = "74", + year = "2000" +} + +@book{Cox1989, + author = "Cox, David A.", + isbn = "0-471-50654-0; 0-471-19079-9", + mrclass = "11A41 (11F11 11R11 11R16 11R18 11R37 11Y11)", + mrnumber = "1028322", + mrreviewer = "Andrew Bremner", + note = "Fermat, class field theory and complex multiplication", + pages = "xiv+351", + publisher = "John Wiley \& Sons, Inc., New York", + series = "{A Wiley-Interscience Publication}", + title = "{Primes of the form {$x^2 + ny^2$}}", + year = "1989" +} + +@book{Hida2013, + author = "Hida, Haruzo", + doi = "10.1007/978-1-4614-6657-4", + isbn = "978-1-4614-6656-7; 978-1-4614-6657-4", + mrclass = "11F11 (11F25 11G15 11G18)", + mrnumber = "3098991", + mrreviewer = "Florian Sprung", + pages = "xviii+449", + publisher = "Springer, New York", + series = "{Springer Monographs in Mathematics}", + title = "{Elliptic curves and arithmetic invariants}", + url = "http://dx.doi.org/10.1007/978-1-4614-6657-4", + year = "2013" +} + +@article{Gamzon2014, + author = "Gamzon, A.", + doi = "10.1142/S1793042114500572", + fjournal = "International Journal of Number Theory", + issn = "1793-0421", + journal = "Int. J. Number Theory", + mrclass = "11G10 (14G20 14K15)", + mrnumber = "3256853", + mrreviewer = "Pete L. Clark", + number = "7", + pages = "1807--1827", + title = "{Local torsion on abelian surfaces with real multiplication by {${\bf Q}(\sqrt{5})$}}", + url = "http://dx.doi.org/10.1142/S1793042114500572", + volume = "10", + year = "2014" +} + +@book{Gamzon2012, + author = "Gamzon, Adam B.", + isbn = "978-1267-49349-1", + mrclass = "Thesis", + mrnumber = "3067899", + note = "Thesis (Ph.D.)--University of Massachusetts Amherst", + pages = "61", + publisher = "ProQuest LLC, Ann Arbor, MI", + title = "{Local torsion on abelian surfaces}", + url = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3518232", + year = "2012" +} + +@book{Mumford2008, + author = "Mumford, David", + isbn = "978-81-85931-86-9; 81-85931-86-0", + mrclass = "14Kxx", + mrnumber = "2514037", + note = "With appendices by C. P. Ramanujam and Yuri Manin, Corrected reprint of the second (1974) edition", + pages = "xii+263", + publisher = "Published for the Tata Institute of Fundamental Research, Bombay; by Hindustan Book Agency, New Delhi", + series = "{Tata Institute of Fundamental Research Studies in Mathematics}", + title = "{Abelian varieties}", + volume = "5", + year = "2008" +} + +@inproceedings{Lenstra1987, + author = "Lenstra, Jr. H. W.", + booktitle = "{Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol. 1, 2 ({B}erkeley, {C}alif., 1986)}", + mrclass = "11Y11 (11G99 11Y05)", + mrnumber = "934218", + mrreviewer = "Samuel S. Wagstaff, Jr.", + pages = "99--120", + publisher = "Amer. Math. Soc., Providence, RI", + title = "{Elliptic curves and number-theoretic algorithms}", + year = "1987" +} + +@article{Lenstra1987_Factoring, + abstract = "This paper is devoted to the description and analysis of a new algorithm to factor positive integers. It depends on the use of elliptic curves. The new method is obtained from Pollard's (p-1)-method (Proc. Cambridge Philos. Soc. 76 (1974), 521-528) by replacing the multiplicative group by the group of points on a random elliptic curve. It is conjectured that the algorithm determines a non-trivial divisor of a composite number n in expected time at most K(p)(log n)2, where p is the least prime dividing n and K is a function for which log $K(x) = \sqrt{(2 + o (1))log x log log x}$ for x → ∞. In the worst case, when n is the product of two primes of the same order of magnitude, this is $exp((1 + o(1))\sqrt{log n log log n})$ (for n → ∞). There are several other factoring algorithms of which the conjectural expected running time is given by the latter formula. However, these algorithms have a running time that is basically independent of the size of the prime factors of n, whereas the new elliptic curve method is substantially faster for small p.", + author = "Lenstra, H. W.", + issn = "0003486X", + journal = "Annals of Mathematics", + number = "3", + pages = "649--673", + publisher = "Annals of Mathematics", + title = "{Factoring Integers with Elliptic Curves}", + url = "http://www.jstor.org/stable/1971363", + volume = "126", + year = "1987" +} + +@book{AtiyahMacdonald1969, + author = "Atiyah, M. F. and Macdonald, I. G.", + mrclass = "13.00", + mrnumber = "0242802", + mrreviewer = "J. A. Johnson", + pages = "ix+128", + publisher = "Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.", + title = "{Introduction to commutative algebra}", + year = "1969" +} + +@book{Milne1980, + author = "Milne, J. S.", + isbn = "0-691-08238-3", + mrclass = "14-02 (14F20 18F99)", + mrnumber = "559531", + mrreviewer = "G. Horrocks", + pages = "xiii+323", + publisher = "Princeton University Press, Princeton, N.J.", + series = "{Princeton Mathematical Series}", + title = "{{\'E}tale cohomology}", + volume = "33", + year = "1980" +} + +@misc{Milne2013, + author = "Milne, J.S.", + note = "Available at www.jmilne.org/math/", + pages = "281+viii", + title = "{Class Field Theory (v4.02)}", + year = "2013" +} + +@misc{stacks-project, + author = "{Stacks Project Authors}, The", + howpublished = "\url{http://stacks.math.columbia.edu}", + shorthand = "Stacks", + title = "{\itshape Stacks Project}", + year = "2016" +} + +@article{Cosgrave2014, + author = "Cosgrave, J. B. and Dilcher, K.", + doi = "10.1007/s10474-013-0357-1", + fjournal = "Acta Mathematica Hungarica", + issn = "0236-5294", + journal = "Acta Math. Hungar.", + mrclass = "11A07 (11B65)", + mrnumber = "3158860", + mrreviewer = "Tatiana Hessami Pilehrood", + number = "1", + pages = "199--230", + title = "{The {G}auss-{W}ilson theorem for quarter-intervals}", + url = "http://dx.doi.org/10.1007/s10474-013-0357-1", + volume = "142", + year = "2014" +} + +@book{Lang1987, + address = "New York, Berlin", + author = "Lang, S.", + isbn = "3-540-96508-4", + note = "Index, bibliogr", + publisher = "Springer", + series = "{Graduate texts in mathematics}", + title = "{Elliptic functions}", + url = "http://opac.inria.fr/record=b1081404", + year = 1987 +} + +@book{CGP2015, + author = "Conrad, B. and Gabber, O. and Prasad, G.", + doi = "10.1017/CBO9781316092439", + edition = "Second", + isbn = "978-1-107-08723-1", + mrclass = "20G15 (14L15)", + mrnumber = "3362817", + pages = "xxiv+665", + publisher = "Cambridge University Press, Cambridge", + series = "{New Mathematical Monographs}", + title = "{Pseudo-reductive groups}", + url = "http://dx.doi.org/10.1017/CBO9781316092439", + volume = "26", + year = "2015" +} + +@article{Deuring1941, + author = "Deuring, M.", + journal = "Abh. Math. Sem. Hansischen Univ.", + mrclass = "09.1X", + mrnumber = "0005125", + mrreviewer = "S. Mac Lane", + pages = "197--272", + title = "{Die {T}ypen der {M}ultiplikatorenringe elliptischer {F}unktionenk{\"o}rper}", + volume = "14", + year = "1941" +} + +@book{Serre1979, + author = "Serre, J.-P.", + isbn = "0-387-90424-7", + mrclass = "12Bxx", + mrnumber = "554237", + note = "Translated from the French by Marvin Jay Greenberg", + pages = "viii+241", + publisher = "Springer-Verlag, New York-Berlin", + series = "{Graduate Texts in Mathematics}", + title = "{Local fields}", + volume = "67", + year = "1979" +} + +@misc{Milne2013, + author = "Milne, J. S.", + note = "Available at www.jmilne.org/math/", + pages = "281+viii", + title = "{Class Field Theory (v4.02)}", + year = "2013" +} + +@misc{stacks-project, + author = "{Stacks Project Authors}, The", + howpublished = "\url{http://stacks.math.columbia.edu}", + shorthand = "Stacks", + title = "{\itshape Stacks Project}", + year = "2016" +} + +@article{Cosgrave2014, + author = "Cosgrave, J. B. and Dilcher, K.", + doi = "10.1007/s10474-013-0357-1", + fjournal = "Acta Mathematica Hungarica", + issn = "0236-5294", + journal = "Acta Math. Hungar.", + mrclass = "11A07 (11B65)", + mrnumber = "3158860", + mrreviewer = "Tatiana Hessami Pilehrood", + number = "1", + pages = "199--230", + title = "{The {G}auss-{W}ilson theorem for quarter-intervals}", + url = "http://dx.doi.org/10.1007/s10474-013-0357-1", + volume = "142", + year = "2014" +} + +@book{Lang1987, + address = "New York, Berlin", + author = "Lang, Serge", + isbn = "3-540-96508-4", + note = "Index, bibliogr", + publisher = "Springer", + series = "{Graduate texts in mathematics}", + title = "{Elliptic functions}", + url = "http://opac.inria.fr/record=b1081404", + year = 1987 +} + +@book{CGP2015, + author = "Conrad, B. and Gabber, O. and Prasad, G.", + doi = "10.1017/CBO9781316092439", + edition = "Second", + isbn = "978-1-107-08723-1", + mrclass = "20G15 (14L15)", + mrnumber = "3362817", + pages = "xxiv+665", + publisher = "Cambridge University Press, Cambridge", + series = "{New Mathematical Monographs}", + title = "{Pseudo-reductive groups}", + url = "http://dx.doi.org/10.1017/CBO9781316092439", + volume = "26", + year = "2015" +} + +@article {Naskrecki2016, + AUTHOR = {Naskr\k{e}cki, B.}, + TITLE = {Divisibility sequences of polynomials and heights estimates}, + JOURNAL = {New York J. Math.}, + FJOURNAL = {New York Journal of Mathematics}, + VOLUME = {22}, + YEAR = {2016}, + PAGES = {989--1020}, + ISSN = {1076-9803}, + MRCLASS = {11G05 (11C08 14H52)}, + MRNUMBER = {3576279}, +MRREVIEWER = {Filip Najman}, +} + +@article{Deuring1941, + author = "Deuring, M.", + journal = "Abh. Math. Sem. Hansischen Univ.", + mrclass = "09.1X", + mrnumber = "0005125", + mrreviewer = "S. Mac Lane", + pages = "197--272", + title = "{Die {T}ypen der {M}ultiplikatorenringe elliptischer {F}unktionenk{\"o}rper}", + volume = "14", + year = "1941" +} + +@article{SY2015, + author = "Sairaiji, F. and Yamauchi, T.", + doi = "10.1016/j.jnt.2015.04.004", + fjournal = "Journal of Number Theory", + issn = "0022-314X", + journal = "J. Number Theory", + mrclass = "11G05 (14G25 14H52)", + mrnumber = "3360340", + mrreviewer = "{\~A}lvaro Lozano-Robledo", + pages = "277--289", + title = "{On the class numbers of the fields of the {$p^n$}-torsion points of certain elliptic curves over {$\mathbb{Q}$}}", + url = "http://dx.doi.org/10.1016/j.jnt.2015.04.004", + volume = "156", + year = "2015" +} + +@article {Hiranouchi, + AUTHOR = {Hiranouchi, T.}, + TITLE = {Local torsion primes and the class numbers associated to an + elliptic curve over {$\Bbb Q$}}, + JOURNAL = {Hiroshima Math. J.}, + FJOURNAL = {Hiroshima Mathematical Journal}, + VOLUME = {49}, + YEAR = {2019}, + NUMBER = {1}, + PAGES = {117--127}, + ISSN = {0018-2079}, + MRCLASS = {11R29 (11G05)}, + MRNUMBER = {3936649}, + MRREVIEWER = {Debopam Chakraborty}, + DOI = {10.32917/hmj/1554516039}, + URL = {https://doi.org/10.32917/hmj/1554516039}, +} + +@article{BGK2005, + author = "Banaszak, G. and Gajda, W. and Kraso{\'n}, P.", + doi = "10.1016/j.jnt.2005.01.008", + fjournal = "Journal of Number Theory", + issn = "0022-314X", + journal = "J. Number Theory", + mrclass = "11G10 (14K15)", + mrnumber = "2180505", + mrreviewer = "Thomas A. Weston", + number = "2", + pages = "322--342", + title = "{Detecting linear dependence by reduction maps}", + url = "http://dx.doi.org/10.1016/j.jnt.2005.01.008", + volume = "115", + year = "2005" +} + +@book{MalleTesterman, + author = "Malle, G. and Testerman, D.", + doi = "10.1017/CBO9780511994777", + isbn = "978-1-107-00854-0", + mrclass = "20G15 (20D06 20G05)", + mrnumber = "2850737", + mrreviewer = "Timothy C. Burness", + pages = "xiv+309", + publisher = "Cambridge University Press, Cambridge", + series = "{Cambridge Studies in Advanced Mathematics}", + title = "{Linear algebraic groups and finite groups of {L}ie type}", + url = "http://dx.doi.org/10.1017/CBO9780511994777", + volume = "133", + year = "2011" +} diff --git a/ramification.fdb_latexmk b/ramification.fdb_latexmk new file mode 100644 index 0000000..93b65dc --- /dev/null +++ b/ramification.fdb_latexmk @@ -0,0 +1,223 @@ +# Fdb version 4 +["pdflatex"] 1730570752.7141 "/Users/aristideskontogeorgis/Library/CloudStorage/Dropbox/Synergates/JedrzejAristides/prearticle/ramification.tex" "ramification.pdf" "ramification" 1730570753.43693 0 + "/Users/aristideskontogeorgis/Library/CloudStorage/Dropbox/Synergates/JedrzejAristides/prearticle/ramification.tex" 1730570752.52224 14900 b66c9efd7adb54653fcefec5fd50125c "" + "/usr/local/texlive/2024/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" + 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