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arXiv · 2004.03847

Differentiability of relative volumes over an arbitrary non-Archimedean field

Sébastien Boucksom·Walter Gubler·Florent Martin
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Abstract

Given an ample line bundle $L$ on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relative volume of two continuous metrics on the Berkovich analytification of $L$, extending previously known results in the discretely valued case. As applications, we provide fundamental solutions to certain non-Archimedean Monge--Amp\`ere equations, and generalize an equidistribution result for Fekete points. Our main technical input comes from determinant of cohomology and Deligne pairings.

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Sébastien Boucksom, Walter Gubler, Florent Martin. 2020-04-08. Differentiability of relative volumes over an arbitrary non-Archimedean field. https://arxiv.org/abs/2004.03847

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