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.
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https://hal.archives-ouvertes.fr/hal-00133410
Contributor : Antoine Chambert-Loir <>
Submitted on : Monday, February 26, 2007 - 11:45:38 AM
Last modification on : Thursday, November 15, 2018 - 11:56:24 AM

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Antoine Chambert-Loir. Mesures et équidistribution sur les espaces de Berkovich. Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2006, 595, pp.215-235. ⟨10.1515/CRELLE.2006.049⟩. ⟨hal-00133410⟩

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