Attaining potentially good reduction in arithmetic dynamics
Number Theory
2015-01-05 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1312.4493,
title = {Attaining potentially good reduction in arithmetic dynamics},
author = {Robert L. Benedetto},
journal= {arXiv preprint arXiv:1312.4493},
year = {2015}
}
Comments
17 pages; added Remark 3.5, on rationality of Julia sets, and Section 5, concerning totally ramified extensions