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arXiv · 2504.16543

The different for base change of arithmetic curves

Art Waeterschoot
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Abstract

We introduce a method for studying reduction types of arithmetic curves and wildly ramified base change. We give new proofs of earlier results of Lorenzini and Obus-Wewers, and resolve a question of Lorenzini on the Euler characteristic of the resolution graph of a $p$-cyclic arithmetic surface quotient singularity. Our method consists of constructing a simultaneous skeleton for the associated cover of Berkovich analytifications and applying a skeletal Riemann-Hurwitz formula.

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Art Waeterschoot. 2025-04-23. The different for base change of arithmetic curves. https://arxiv.org/abs/2504.16543

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