A criterion for potentially good reduction in nonarchimedean dynamics

Robert L. Benedetto

Acta Arithmetica (2014)

  • Volume: 165, Issue: 3, page 251-256
  • ISSN: 0065-1036

Abstract

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Let K be a nonarchimedean field, and let ϕ ∈ 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 ϕ and their preimages, that determines whether or not the dynamical system ϕ: ℙ¹ → ℙ¹ has potentially good reduction.

How to cite

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Robert L. Benedetto. "A criterion for potentially good reduction in nonarchimedean dynamics." Acta Arithmetica 165.3 (2014): 251-256. <http://eudml.org/doc/279795>.

@article{RobertL2014,
abstract = {Let K be a nonarchimedean field, and let ϕ ∈ 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 ϕ and their preimages, that determines whether or not the dynamical system ϕ: ℙ¹ → ℙ¹ has potentially good reduction.},
author = {Robert L. Benedetto},
journal = {Acta Arithmetica},
keywords = {arithmetic dynamics; good reduction; periodic points},
language = {eng},
number = {3},
pages = {251-256},
title = {A criterion for potentially good reduction in nonarchimedean dynamics},
url = {http://eudml.org/doc/279795},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Robert L. Benedetto
TI - A criterion for potentially good reduction in nonarchimedean dynamics
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 3
SP - 251
EP - 256
AB - Let K be a nonarchimedean field, and let ϕ ∈ 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 ϕ and their preimages, that determines whether or not the dynamical system ϕ: ℙ¹ → ℙ¹ has potentially good reduction.
LA - eng
KW - arithmetic dynamics; good reduction; periodic points
UR - http://eudml.org/doc/279795
ER -

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