Mesures et équidistribution sur les espaces de Berkovich

Details Mesures et équidistribution sur les espaces de Berkovich Mesures et équidistribution sur les espaces de Berkovich

2003-04-02

arxiv.org/abs/math/0304023v3

J. Reine Angew. Math. 595 (2006), 215--235

Mathematics

Number Theory

In French; submitted

Scientific paper

10.1515/CRELLE.2006.049

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.

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