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arXiv · 2511.21835

Metrized ample line bundles in non-Archimedean geometry II

Yanbo Fang
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Abstract

We introduce a class of semipositive metrics on ample line bundles in non-Archimedean geometry, called Shilov finite metrics. We calculate the determinant metric distorsion in the exact sequence induced by a global section using non-Archimedean norm reduction techniques. This leads to an analytic proof to the arithmetic Hilbert-Samuel formula over a local place for a semipositively metrized ample line bundle. We define the equidistribution measure associated to a Shilov finite metric and solve the corresponding inverse problem.

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Yanbo Fang. 2025-11-26. Metrized ample line bundles in non-Archimedean geometry II. https://arxiv.org/abs/2511.21835

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