Uniform bounds for pre-periodic points in families of twists

2012/04/19 by Alon Y. Levy, Levy, Alon, Michelle Manes +3
Computer Science · Mathematics · #11 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1204.4447

openalex publication_date 2012/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Questions on self maps of algebraic varieties

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