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arXiv · 1312.4493

Attaining potentially good reduction in arithmetic dynamics

Robert L. Benedetto
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Abstract

Let K be a non-archimedean field, and let f in K(z) be a rational function of degree d>1. If f has potentially good reduction, we give an upper bound, depending only on d, for the minimal degree of an extension L/K such that f is conjugate over L to a map of good reduction. In particular, if d=2 or d is greater than the residue characteristic of K, the bound is d+1. If K is discretely valued, we give examples to show that our bound is sharp.

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Robert L. Benedetto. 2013-12-16. Attaining potentially good reduction in arithmetic dynamics. https://arxiv.org/abs/1312.4493

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