S-integral preperiodic points for dynamical systems over number fields

Details S-integral preperiodic points for dynamical systems over number fields S-integral preperiodic points for dynamical systems over number fields

2007-09-25

arxiv.org/abs/0709.3879v2

Mathematics

Number Theory

Fixed some typos and an incorrect reference

Scientific paper

Given a rational map $\phi: {\mathbb P}^1\to {\mathbb P}^1$ defined over a
number field $K$, we prove a finiteness result for $\phi$-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.

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