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arXiv · 2509.10633

Effective Artin-Schreier-Witt theory for curves

Christophe Levrat·Rubén Muñoz--Bertrand
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Abstract

We present an algorithm which, given a connected smooth projective curve $X$ over an algebraically closed field of characteristic $p>0$ and its Hasse--Witt matrix, as well as a positive integer $n$, computes all \'etale Galois covers of $X$ with group $\mathbb{Z}/p^n\mathbb{Z}$. We compute the complexity of this algorithm when $X$ is defined over a finite field, and provide a complete implementation in SageMath, as well as some explicit examples. We then apply this algorithm to the computation of the cohomology complex of a locally constant sheaf of $\mathbb{Z}/p^n\mathbb{Z}$-modules on such a curve.

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BibTeXRIS

Christophe Levrat, Rubén Muñoz--Bertrand. 2025-09-12. Effective Artin-Schreier-Witt theory for curves. https://arxiv.org/abs/2509.10633

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