Mesures et équidistribution sur les espaces de Berkovich

Abstract

The proof by Ullmo and Zhang of Bogomolov's conjecture about points of small height in abelian varieties made a crucial use of an equidistribution property for ``small points'' in the associated complex abelian variety. We study the analogous equidistribution property at $p$-adic places. Our results can be conveniently stated within the framework of the analytic spaces defined by Berkovich. The first one is valid in any dimension but is restricted to ``algebraic metrics'', the second one is valid for curves, but allows for more general metrics, in particular to the normalized heights with respect to dynamical systems.

In French; submitted

Cited by in corpus (15)

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• The Dynamical Andre-Oort Conjecture: Unicritical Polynomials
• Néron-Tate heights of cycles on jacobians
• Abelian extensions in dynamical Galois theory
• Theta-Induced Diffusion on Tate Elliptic Curves over Non-Archimedean Local Fields
• p-adic equidistribution of CM points
• Heights of hypersurfaces in toric varieties
• Algebraic zeros divisors on the projective line having small diagonals and small heights and their application to adelic dynamics
• The arithmetic Hodge Index Theorem and rigidity of dynamical systems over function fields
• Quantitative equidistribution of Galois orbits of small points in the N-dimensional torus
• Parabolic bifurcation loci in the spaces of rational functions
• Monge-Ampère measures for toric metrics on abelian varieties