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arXiv · 0801.4503

Non-archimedean canonical measures on abelian varieties

Walter Gubler
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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 $c_1(L|_X)^{\wedge d}$ 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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Walter Gubler. 2009-12-09. Non-archimedean canonical measures on abelian varieties. https://doi.org/10.1112/s0010437x09004679

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