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Differentiability of non-archimedean volumes and non-archimedean Monge�Amp�re equations\n (with an appendix by Robert Lazarsfeld)

Gubler, Walter


Let X be a normal projective variety over a complete discretely valued field and L a line bundle on X. We denote by X-an the analytification of X in the sense of Berkovich and equip the analytification L-an of L with a continuous metric parallel to parallel to. We study non-archimedean volumes, a tool which allows us to control the asymptotic growth of small sections of big powers of L. We prove ...


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