Journal article
Galois structure of the holomorphic differentials of curves
Journal of number theory, Vol.216, pp.1-68
11/2020
DOI: 10.1016/j.jnt.2020.04.015
Abstract
Let X be a smooth projective geometrically irreducible curve over a perfect field k of positive characteristic p. Suppose G is a finite group acting faithfully on X such that G has non-trivial cyclic Sylow p-subgroups. We show that the decomposition of the space of holomorphic differentials of X into a direct sum of indecomposable k[G]-modules is uniquely determined by the lower ramification groups and the fundamental characters of closed points of X that are ramified in the cover X⟶X/G. We apply our method to determine the PSL(2,Fℓ)-module structure of the space of holomorphic differentials of the reduction of the modular curve X(ℓ) modulo p when p and ℓ are distinct odd primes and the action of PSL(2,Fℓ) on this reduction is not tamely ramified. This provides some non-trivial congruences modulo appropriate maximal ideals containing p between modular forms arising from isotypic components with respect to the action of PSL(2,Fℓ) on X(ℓ).
Details
- Title: Subtitle
- Galois structure of the holomorphic differentials of curves
- Creators
- Frauke M Bleher - University of IowaTed Chinburg - University of PennsylvaniaAristides Kontogeorgis - National and Kapodistrian University of Athens
- Resource Type
- Journal article
- Publication Details
- Journal of number theory, Vol.216, pp.1-68
- DOI
- 10.1016/j.jnt.2020.04.015
- ISSN
- 0022-314X
- eISSN
- 1096-1658
- Publisher
- Elsevier Inc
- Grant note
- DMS-1801328 / NSF (https://doi.org/10.13039/100000001) DMS-1360767 / NSF (https://doi.org/10.13039/100000001) DMS-1360621 / NSF (https://doi.org/10.13039/100000001) CNS-1513671; CNS-1701785 / NSF (https://doi.org/10.13039/100000001) 338379 / Simons Foundation (https://doi.org/10.13039/100000893)
- Language
- English
- Date published
- 11/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984241051102771
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