Skip to main content
Article thumbnail
Location of Repository

On some notions of good reduction for endomorphisms of the projective line

By Jung Kyu Canci, Giulio Peruginelli and Dajano Tossici

Abstract

Let $\Phi$ be an endomorphism of $\SR(\bar{\Q})$, the projective line over the algebraic closure of $\Q$, of degree $\geq2$ defined over a number field $K$. Let $v$ be a non-archimedean valuation of $K$. We say that $\Phi$ has critically good reduction at $v$ if any pair of distinct ramification points of $\Phi$ do not collide under reduction modulo $v$ and the same holds for any pair of branch points. We say that $\Phi$ has simple good reduction at $v$ if the map $\Phi_v$, the reduction of $\Phi$ modulo $v$, has the same degree of $\Phi$. We prove that if $\Phi$ has critically good reduction at $v$ and the reduction map $\Phi_v$ is separable, then $\Phi$ has simple good reduction at $v$.Comment: 15 page

Topics: Mathematics - Number Theory, Mathematics - Algebraic Geometry, 14H25, 37P05, 37P35
Year: 2011
OAI identifier: oai:arXiv.org:1103.3853
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1103.3853 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.