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Semistable reduction of covers of degree $p$

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arxiv 2404.16105 v2 pith:EWMNBQ7U submitted 2024-04-24 math.NT math.AG

classification math.NTmath.AG
keywords reductioncoverscurvesdegreesemistableanalyticapproachattention
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Semistable Reduction of Plane Quartics

    math.AG 2025-11 conditional novelty 7.0 of 10

    A plane quartic admits a GIT-stable plane model exactly when its stable reduction is non-hyperelliptic, and then the stable model is the unique minimal semistable model arising by resolving the cusps of the GIT model.

  2. Semistable reduction of smooth quartics

    math.AG 2026-06 conditional novelty 4.0 of 10

    For smooth plane quartics, non-hyperelliptic stable reduction is equivalent to the existence of a unique GIT-stable plane model, and the stable model is obtained by cusp resolution.

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