-group Galois covers of curves in characteristic . II

  • Jędrzej Garnek

    Adam Mickiewicz University, Poznań, Poland
$p$-group Galois covers of curves in characteristic $p$. II cover
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Abstract

Let be an algebraically closed field of characteristic and let be a finite -group. The results of Harbater, Katz and Gabber associate to every -linear action of on an HKG-cover, i.e. a -cover of the projective line ramified only over . 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 . 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 .

Cite this article

Jędrzej Garnek, -group Galois covers of curves in characteristic . II. Doc. Math. 30 (2025), no. 2, pp. 347–377

DOI 10.4171/DM/998