Uniform bounds for preperiodic points in families of twists
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(2014)
摘要
Let phi be a morphism of P-N defined over a number field K. We prove that there is a bound B depending only on f such that every twist of phi has no more than B K-rational preperiodic points. (This result is analogous to a result of Silverman for abelian varieties.) For two specific families of quadratic rational maps over Q, we find the bound B explicitly.
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