Uniform bounds for preperiodic points in families of twists
Abstract
Let phi be a morphism of projective Nspace defined over a number field K. We prove that there is a bound B depending only on phi such that every twist of phi has no more than B Krational preperiodic points. (This result is analagous to a result of Silverman for abelian varieties.) For two specific families of quadratic rational maps over Q, we find the bound B explicitly.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1204.4447
 Bibcode:
 2012arXiv1204.4447L
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Dynamical Systems;
 11
 EPrint:
 12 pages, 2 figures