$p$-group Galois covers of curves in characteristic $p$. II
Year: 2025
Type: article
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 to every k -linear action of G on k\llbracket t\rrbracket an HKG-cover, i.e. a G -cover of the projective line ramified only over \infty . 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 G . 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 .
Source: Documenta Mathematica
DOI: 10.4171/dm/998
Author: Jędrzej Garnek
Institution: Adam Mickiewicz University in Poznań
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408670126