Non-archimedean canonical measures on abelian varieties

Abstract

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 ) ∧ 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.