𝑝-group Galois covers of curves in characteristic 𝑝

Garnek, Jędrzej

doi:10.1090/tran/8932

$p$-group Galois covers of curves in characteristic $p$
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by Jędrzej Garnek

Trans. Amer. Math. Soc. 376 (2023), 5857-5897

DOI: https://doi.org/10.1090/tran/8932

Published electronically: May 17, 2023

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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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