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A criterion for potentially good reduction in nonarchimedean dynamics

Volume 165 / 2014

Robert L. Benedetto Acta Arithmetica 165 (2014), 251-256 MSC: Primary 37P05; Secondary 37P20, 11S82. DOI: 10.4064/aa165-3-4

Abstract

Let $K$ be a nonarchimedean field, and let $\phi \in K(z)$ be a polynomial or rational function of degree at least $2$. We present a necessary and sufficient condition, involving only the fixed points of $\phi $ and their preimages, that determines whether or not the dynamical system $\phi :\mathbb {P}^1\to \mathbb {P}^1$ has potentially good reduction.

Authors

  • Robert L. BenedettoDepartment of Mathematics and Statistics
    Amherst College
    Amherst, MA 01002, U.S.A.
    e-mail

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