de_rham_cyclic/AKGeneral.bib

#Created by Kbib version 0.6.1
#Last modified: Fri Sep 14 11:11:37 2007


@preamble{
   " \def\cprime{$'$} "
}

@string{ABHMS={Abh. Math. Sem. Univ. Hamburg}}

@string{ABSAM={Abstracts Amer. Math. Soc.}}

@string{ACTAA1={Acta Arith.}}

@string{ADVAM2={Adv. in Math.}}

@string{ALGEL1={Algebra and Logic}}

@string{AMEMM={Amer. Math. Monthly}}

@string{AMS={American Mathematical Society, Providence, Rhode Island}}

@string{ANNMA2={Ann. of Math.}}

@string{AP={Academic Press, London - New York}}

@string{AW={Addison Wesley, Reading, Mass.}}

@string{BULAM3={Bull. Amer. Math. Soc. (N.S.)}}

@string{BULLM={Bull. London Math. Soc.}}

@string{COMMA2={Comm. Algebra}}

@string{COMMA3={Comput. Math. Appl.}}

@string{COMMH={Comment. Math. Helv.}}

@string{COMPO={Compositio Math.}}

@string{CRACA1={C. R. Acad. Sci. Paris S{\'e}r. I Math.}}

@string{CUP={Cambridge University Press, Cambridge}}

@string{ENSEM2={Enseign. Math. (2)}}

@string{GTM={Graduate Texts in Math.}}

@string{Grundlehren={Grundlehren der Math.\ Wiss.}}

@string{INSHE={Inst. Hautes {\'E}tudes Sci. Publ. Math.}}

@string{INTJM4={Internat. J. Math. Math. Sci.}}

@string{INVEM={Invent. Math.}}

@string{JALGE={J. Algebra}}

@string{JAMEM={J. Amer. Math. Soc.}}

@string{JGEOM2={J. Geom.}}

@string{JLONM2={J. London Math. Soc. (2)}}

@string{JNUMT={J. Number Theory}}

@string{JPURA1={J. Pure Appl. Algebra}}

@string{JREIA={J. Reine Angew. Math.}}

@string{LNM={Lecture Notes in Math.}}

@string{MANUM={Manuscripta Math.}}

@string{MATHA={Math. Ann.}}

@string{MATHC3={Math. Comp.}}

@string{MATHI={Math. Intelligencer}}

@string{MATHS1={Math. Scand.}}

@string{MATHZ={Math. Z.}}

@string{MATPC={Math. Proc. Cambridge Philos. Soc.}}

@string{MATUS={Math. USSR-Sb.}}

@string{MEMAM={Mem. Amer. Math. Soc.}}

@string{NAGMJ={Nagoya Math. J.}}

@string{NEDAW2={Nederl. Akad. Wetensch. Proc. Ser. A}}

@string{NIEAW3={Nieuw Arch. Wisk. (4)}}

@string{NOTAM={Notices Amer. Math. Soc.}}

@string{PACJM={Pacific J. Math.}}

@string{PHITRA={Philos. Trans. Roy. Soc. London Ser. A}}

@string{PROAM={Proc. Amer. Math. Soc.}}

@string{PROEM={Proc. Edinburgh Math. Soc. Edinburgh Math. Notes}}

@string{PROEM2={Proc. Edinburgh Math. Soc. (2)}}

@string{PROLM2={Proc. London Math. Soc. (3)}}

@string{PUP={Princeton University Press, Princeton - New Jersey}}

@string{S={Springer, Berlin - Heidelberg - New York}}

@string{TRAAM={Trans. Amer. Math. Soc.}}

@string{UTM={Undergraduate Texts in Math.}}

@string{WILEY={John Wiley \& Sons, New York - Chichester}}

@article {maxcovered-max,
    AUTHOR = {Lachaud, Gilles},
     TITLE = {Sommes d'{E}isenstein et nombre de points de certaines courbes
              alg\'ebriques sur les corps finis},
   JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences.
              S\'erie I. Math\'ematique},
    VOLUME = {305},
      YEAR = {1987},
    NUMBER = {16},
     PAGES = {729--732},
      ISSN = {0249-6291},
     CODEN = {CASMEI},
   MRCLASS = {11G20 (11L05 11T71 14G15 94B05)},
  MRNUMBER = {MR920053 (88m:11044)},
MRREVIEWER = {Kenneth A. 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},
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      YEAR = {1990},
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}



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@article {Komiya,
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@book{RitzNotes,
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@article{Torres00,
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	number = {},
	pages = {},
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	fjournal = {},
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	mrclass = {},
	mrnumber = {},
	mrreviewer = {}
}
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@article{KoANT,
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	year = 1998,
	volume = {72},
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	pages = {110--136},
	file = {/home/kontogar/Papers/pdf/D1.pdf},
	coden = {JNUTA9},
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	issn = {0022-314X}
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characteristic 0. However there are exceptional cases, namely characteristic p>0
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group is given.      1996 Academic Press, Inc.},
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 PUBLISHER = {Springer-Verlag},
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@article{Roq:70,
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@book{SeGalCoh,
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@book{SeL,
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}

@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}
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@book{Kodaira2005,
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	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 $p>0$.},
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      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
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   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
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   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},
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  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
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              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},
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  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},
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  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},
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    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,
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  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.},
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  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},
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              {V}ol. {I}},
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    VOLUME = {67},
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  MRNUMBER = {3525467},
MRREVIEWER = {Haohao Wang},
}

@article {MR1273472,
    AUTHOR = {Bayer, Dave and Eisenbud, David},
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@incollection {MR524365,
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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,
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  MRNUMBER = {2768284},
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@book {VakilSea,
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@book {MR2014407,
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}

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@incollection {MR555696,
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              {C}openhagen, {C}openhagen, 1978)},
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}

@book {MR0354657,
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@book {MR1363949,
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}

@book {MR2894984,
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      YEAR = {2012},
     PAGES = {xiv+454},
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  MRNUMBER = {2894984},
}

@article {MR3361016,
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}



@article {MR494707,
    AUTHOR = {Goto, Shiro and Watanabe, Keiichi},
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}

@book {MR0274461,
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@book {MR2560561,
    AUTHOR = {Peeva, Irena},
     TITLE = {Graded syzygies},
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     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},
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    VOLUME = {724},
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      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},
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      YEAR = {1985},
   MRCLASS = {14H45 (14C20)},
  MRNUMBER = {895152},
MRREVIEWER = {Ciro Ciliberto},
}

@book {MR2267317,
    AUTHOR = {Benson, David J.},
     TITLE = {Modular representation theory},
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      NOTE = {New trends and methods,
              Second printing of the 1984 original},
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      YEAR = {2006},
     PAGES = {xii+231},
      ISBN = {978-3-540-13389-6; 3-540-13389-5},
   MRCLASS = {20C20 (20-01)},
  MRNUMBER = {2267317},
}

@article {MR3069500,
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  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t
              Hamburg},
    VOLUME = {6},
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      ISSN = {0025-5858},
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  MRNUMBER = {3069500},
       DOI = {10.1007/BF02940613},
       URL = {https://doi.org/10.1007/BF02940613},
}




@article {1901.08446,
    AUTHOR = {Kontogeorgis, Aristides and Tsouknidas, Ioannis},
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       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},
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    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},
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    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},
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    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.},
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   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {36},
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  MRNUMBER = {0314846 (47 \#3396)},
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}

@article {DrinTor,
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  FJOURNAL = {Akademija Nauk SSSR. Funkcional\cprime nyi Analiz i ego
              Prilo\v zenija},
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    NUMBER = {2},
     PAGES = {83--84},
      ISSN = {0374-1990},
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MRREVIEWER = {K.-B. Gundlach},
}

@article {RosenNorm,
    AUTHOR = {Rosen, Michael},
     TITLE = {The norm map on {J}acobians},
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     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,
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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},
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              properties ({P}roc. {S}ympos., {U}niv. {D}urham, {D}urham,
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     PAGES = {193--268},
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   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},
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  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {496},
      YEAR = {1998},
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      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
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    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,
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  FJOURNAL = {Mathematische Annalen},
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      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},
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      YEAR = {1980},
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       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},
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     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},
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      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,
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     TITLE = {Galois structure of the holomorphic differentials of curves},
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      YEAR = {2020},
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      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,
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 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},
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    NUMBER = {3},
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      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
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 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},
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  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.},
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    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},
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      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
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   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.},
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@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},
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@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}
}



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@book {MR717033,
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}

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    VOLUME = {1960/61},
 PUBLISHER = {Institut des Hautes \'{E}tudes Scientifiques, Paris},
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  MRNUMBER = {0217087},
}

@misc{SGA1a,
Author = {Alexander Grothendieck and Michele Raynaud},
Title = {Revêtements étales et groupe fondamental (SGA 1)},
Year = {2002},
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}

@article {MR2254623,
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    NUMBER = {3},
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      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,
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   MRCLASS = {14G20 (11S31 13F25 14H30 14H37 14L30)},
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MRREVIEWER = {Daniel Barsky},
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       URL = {https://doi.org/10.1007/s00208-009-0374-0},
}

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   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
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}






@book {MR506881,
    AUTHOR = {Hazewinkel, Michiel},
     TITLE = {Formal groups and applications},
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 PUBLISHER = {Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers],
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      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},
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    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},
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    VOLUME = {139},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {443--490},
      ISSN = {0003-486X},
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  MRNUMBER = {1274097},
MRREVIEWER = {Boas Erez},
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       URL = {https://doi.org/10.2307/2946586},
}

@article{Chinburg1996TameAO,
  title={Tame actions of group schemes: integrals and slices},
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}

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      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,
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 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
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      ISBN = {978-1-107-60262-5},
   MRCLASS = {05-02 (05A15 06-02)},
  MRNUMBER = {2868112},
}

@book {MR1251956,
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 PUBLISHER = {Cambridge University Press, Cambridge},
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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,
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     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,
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  FJOURNAL = {Compositio Mathematica},
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    NUMBER = {3},
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  MRNUMBER = {1818984},
MRREVIEWER = {Richard P. Thomas},
       DOI = {10.1023/A:1002470302976},
       URL = {https://doi.org/10.1023/A:1002470302976},
}


@inproceedings {MR1403918,
    AUTHOR = {Kontsevich, Maxim},
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              {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},
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    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,
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      YEAR = {1984},
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       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)},
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       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},
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    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},
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 BOOKTITLE = {Higher-dimensional geometry over finite fields},
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    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},
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      YEAR = {1997},
    NUMBER = {2},
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      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,
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              schemes},
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  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},
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   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.},
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    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},
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  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},
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    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},
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 PUBLISHER = {Springer Spektrum, Wiesbaden},
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@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,
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@book {MR3408060,
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  Key          = {SageMath},
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  note         = {{\tt https://www.sagemath.org}},
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}

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@book {Pragmatiki,
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@book {Elements,
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@misc{ConradAlgebra,
  author = "Keith Conrad",
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@misc{Khim,
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@masterthesis{Asterios,
  author = {Γκαντζουνης, Αστέριος},
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}


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@book{pixor,
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  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}, 
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      archivePrefix={arXiv},
      primaryClass={math.AG}
}

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@book {MR1410264,
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@MISC {152738,
    TITLE = {The fibre product of two quotient stacks},
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@book {MR2035696,
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}