p-group Galois covers of curves in characteristic p II

2023/08/25 by Garnek, Jędrzej · 1 citation
#14F40 #14G17 #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2308.13290

Abstract

Let k be an algebraically closed field of characteristic p > 0 and let G be a finite p-group. The results of Harbater, Katz and Gabber associate a G-cover of the projective line ramified only over ∞ to every k-linear action of G on k[[t]]. In this paper we relate the HKG-covers to the classical problem of determining the equivariant structure of cohomologies of a curve with an action of a p-group. To this end, we present a new way of computing cohomologies of HKG-covers. As an application of our results, we compute the equivariant structure of the de Rham cohomology of Klein four covers in characteristic 2.

Cited by

• On the de Rham cohomology of cyclic covers

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• p-group Galois covers of curves in characteristic p
• The de Rham cohomology of covers with cyclic p-Sylow subgroup
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• A relative Shafarevich theorem
• A note on Galois modules and the algebraic fundamental group of projective curves