Non-archimedean canonical measures on abelian varieties

Details Non-archimedean canonical measures on abelian varieties Non-archimedean canonical measures on abelian varieties

2008-01-29

arxiv.org/abs/0801.4503v3

Compositio Math. 146, 683-730 (2010)

Mathematics

Number Theory

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

Scientific paper

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.

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