Uniform bounds for preperiodic points in families of twists

@inproceedings{Levy2012UniformBF,
  title={Uniform bounds for preperiodic points in families of twists},
  author={Alon Y. Levy and Michelle Manes and Bianca Thompson},
  year={2012}
}
Letbe a morphism of PN defined over a number field K. We prove that there is a bound B depending only onsuch that every twist of � has no more than B K-rational preperiodic points. (This result is analagous to a result of Silverman for abelian varieties (10).) For two specific families of quadratic rational maps over Q, we find the bound B explicitly. 

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