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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.10633 |
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| _version_ | 1866911152627253248 |
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| author | Levrat, Christophe Muñoz--Bertrand, Rubén |
| author_facet | Levrat, Christophe Muñoz--Bertrand, Rubén |
| contents | 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 étale 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective Artin-Schreier-Witt theory for curves Levrat, Christophe Muñoz--Bertrand, Rubén Number Theory Algebraic Geometry 11Y16, 11G20, 14F20, 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 étale 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. |
| title | Effective Artin-Schreier-Witt theory for curves |
| topic | Number Theory Algebraic Geometry 11Y16, 11G20, 14F20, |
| url | https://arxiv.org/abs/2509.10633 |