Dynamique analytique sur Z. II : Écart uniforme entre Lattès et conjecture de Bogomolov-Fu-Tschinkel

2022/07/04 by Jérôme Poineau, Poineau, Jérôme
Mathematics · #11G05 #11G50 #14G22 #37P15 #37P50 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2207.01574

openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the mutual energy (or the intersection product in the sense of Arakelov theory) of two dynamical systems associated to Lattès morphisms over Q is uniformly bounded below and deduce a proof of a conjecture of Bogomolov-Fu-Tschinkel: the number of common images of torsion points of two non-isomorphic elliptic curves over C by a standard morphism to the projective line is uniformly bounded. The proof crucially relies on the theory of Berkovich spaces over Z and on an original argument allowing to obtain a global estimate from a central estimate (over a trivially valued field).

Cited by

• Dynamique analytique sur Z. I : Mesures d'équilibre sur une droite projective relative

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