A criterion for potentially good reduction in nonarchimedean dynamics
Volume 165 / 2014
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.
