English

A Criterion for Potentially Good Reduction in Non-archimedean Dynamics

Number Theory 2013-12-03 v2 Dynamical Systems

Abstract

Let K be a non-archimedean field, and let f 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 f and their preimages, that determines whether or not the dynamical system f on P^1 has potentially good reduction.

Keywords

Cite

@article{arxiv.1311.6695,
  title  = {A Criterion for Potentially Good Reduction in Non-archimedean Dynamics},
  author = {Robert L. Benedetto},
  journal= {arXiv preprint arXiv:1311.6695},
  year   = {2013}
}

Comments

7 pages; typos corrected and a little extra commentary added

R2 v1 2026-06-22T02:15:12.095Z