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arXiv · 2404.16105

Semistable reduction of covers of degree $p$

Ole Ossen
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Abstract

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.

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Ole Ossen. 2024-04-24. Semistable reduction of covers of degree $p$. https://arxiv.org/abs/2404.16105

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