Non-archimedean canonical measures on abelian varieties

Publisher: Cambridge University Press

E-ISSN: 1570-5846|146|3|683-730

ISSN: 0010-437x

Source: Compositio Mathematica, Vol.146, Iss.3, 2010-05, pp. : 683-730

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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 c1(LX)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.