p-group Galois covers of curves in characteristic p

2022/01/13 by Jędrzej Garnek, Garnek, Jędrzej · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2201.04861

Abstract

We study cohomologies of a curve with an action of a finite p-group over a field of characteristic p. Assuming the existence of a certain 'magical element' in the function field of the curve, we compute the equivariant structure of the module of holomorphic differentials and the de Rham cohomology, up to certain local terms. We show that a generic p-group cover has a 'magical element'. As an application we compute the de Rham cohomology of a curve with an action of a finite cyclic group of prime order.

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• On the de Rham cohomology of cyclic covers
• Holomorphic differentials of alternating four covers
• On the cohomological representations of finite automorphism groups of singular curves and compact complex spaces

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