Geodesic
$p$-group Galois covers of curves in characteristic $p$. II
Documenta mathematica, Tome 30 (2025) no. 2, pp. 347-377

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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[[t]] an HKG-cover, i.e. a G-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 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.
DOI : 10.4171/dm/998
Classification : 14F40, 14G17, 14H30
Mots-clés : de Rham cohomology, algebraic curves, group actions, characteristic p 
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     title = {$p$-group {Galois} covers of curves in characteristic~$p${.~II}},
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Jędrzej Garnek. $p$-group Galois covers of curves in characteristic $p$. II. Documenta mathematica, Tome 30 (2025) no. 2, pp. 347-377. doi: 10.4171/dm/998

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