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An analog to Deuring's criterion for good reduction of elliptic curves

Claus Lehr
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Abstract

In this paper we study the reduction of $p$-cyclic covers of the $p$-adic line ramified at exactly four points. For $p=2$ these covers are elliptic curves and Deuring has given a criterion for when such a curve has good reduction. Here we consider the case of $p>2$ and completely determine the stable model of the cover. In particular we obtain a finite extension $R'$ of $R$ necessary for the stable reduction to be defined. No additional conditions are imposed on the geometry of the branch locus and thus this work can be viewed as a first step towards understanding the situation where branch points coalesce.

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Claus Lehr. 2004-09-25. An analog to Deuring's criterion for good reduction of elliptic curves. https://arxiv.org/abs/math/0409493

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