\begin{thebibliography}{1} \bibitem{Bleher_Chinburg_Kontogeorgis_Galois_structure} F.~M. Bleher, T.~Chinburg, and A.~Kontogeorgis. \newblock Galois structure of the holomorphic differentials of curves. \newblock {\em J. Number Theory}, 216:1--68, 2020. \bibitem{Curtis_Reiner_Methods_II} C.~W. Curtis and I.~Reiner. \newblock {\em Methods of representation theory. {V}ol. {II}}. \newblock Pure and Applied Mathematics (New York). John Wiley \& Sons, Inc., New York, 1987. \newblock With applications to finite groups and orders, A Wiley-Interscience Publication. \bibitem{Garnek_equivariant} J.~Garnek. \newblock Equivariant splitting of the {H}odge-de {R}ham exact sequence. \newblock {\em Math. Z.}, 300(2):1917--1938, 2022. \bibitem{garnek_indecomposables} J.~Garnek. \newblock Indecomposable direct summands of cohomologies of curves, 2024. \newblock arXiv 2410.03319. \bibitem{Hartshorne1977} R.~Hartshorne. \newblock {\em {Algebraic geometry}}. \newblock Springer-Verlag, New York-Heidelberg, 1977. \newblock Graduate Texts in Mathematics, No. 52. \bibitem{Serre1979} J.-P. Serre. \newblock {\em {Local fields}}, volume~67 of {\em {Graduate Texts in Mathematics}}. \newblock Springer-Verlag, New York-Berlin, 1979. \newblock Translated from the French by Marvin Jay Greenberg. \bibitem{Valentini_Madan_Automorphisms} R.~C. Valentini and M.~L. Madan. \newblock Automorphisms and holomorphic differentials in characteristic~{$p$}. \newblock {\em J. Number Theory}, 13(1):106--115, 1981. \end{thebibliography}