Non-archimedean canonical measures on abelian varieties

Abstract

For a closed d-dimensional subvariety X of an abelian variety A and a canonically metrized line bundle L on A, Chambert-Loir has introduced measures $c_1(L{|}_X{)}^{\wedge d}$ on the Berkovich analytic space associated to A with respect to the discrete valuation of the ground field. In this paper, we give an explicit description of these canonical measures in terms of convex geometry. We use a generalization of the tropicalization related to the Raynaud extension of A and Mumford's construction. The results have applications to the equidistribution of small points.

Thorough revision according to the comments of the referee. To appear in Compositio

References in corpus (4)

• Big Line Bundles over Arithmetic Varieties
• The Bogomolov conjecture for totally degenerate abelian varieties
• Tropical varieties for non-archimedean analytic spaces
• Non-archimedean canonical measures on abelian varieties

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