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arXiv · 1204.4447

Uniform bounds for pre-periodic points in families of twists

Alon Levy·Michelle Manes·Bianca Thompson
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Abstract

Let phi be a morphism of projective N-space 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 K-rational 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.

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Alon Levy, Michelle Manes, Bianca Thompson. 2012-04-19. Uniform bounds for pre-periodic points in families of twists. https://arxiv.org/abs/1204.4447

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