S-integral preperiodic points for dynamical systems over number fields

Abstract

Given a rational map $\varphi :{\mathbb{P}}^1\to {\mathbb{P}}^1$ defined over a number field $K$, we prove a finiteness result for $\varphi$-preperiodic points which are $S$-integral with respect to a non-preperiodic point $P$, provided $P$ satisfies a certain local condition at each place. This verifies a special case of a conjecture of S. Ih.

Fixed some typos and an incorrect reference

Cited by in corpus (1)

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