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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2404.16105 |
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| _version_ | 1866910536392769536 |
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| author | Ossen, Ole |
| author_facet | Ossen, Ole |
| contents | Let $K$ be a local field of residue characteristic $p>0$. We explain how to compute the semistable reduction of $K$-curves $Y$ equipped with a degree-$p$ morphism from $Y$ to the projective line. This includes the reduction at $p$ of superelliptic curves of degree $p$, but our approach is not limited to Galois covers. We give particular attention to the reduction of plane quartics at $p=3$, which case is implemented in SageMath. We use the language of non-archimedean analytic geometry in the sense of Berkovich. A key tool is the different function of Cohen, Temkin, and Trushin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semistable reduction of covers of degree $p$ Ossen, Ole Number Theory Algebraic Geometry 11G20, 14H25 Let $K$ be a local field of residue characteristic $p>0$. We explain how to compute the semistable reduction of $K$-curves $Y$ equipped with a degree-$p$ morphism from $Y$ to the projective line. This includes the reduction at $p$ of superelliptic curves of degree $p$, but our approach is not limited to Galois covers. We give particular attention to the reduction of plane quartics at $p=3$, which case is implemented in SageMath. We use the language of non-archimedean analytic geometry in the sense of Berkovich. A key tool is the different function of Cohen, Temkin, and Trushin. |
| title | Semistable reduction of covers of degree $p$ |
| topic | Number Theory Algebraic Geometry 11G20, 14H25 |
| url | https://arxiv.org/abs/2404.16105 |