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arXiv · 2503.14099

A local version of the arithmetic Hodge index theorem over quasiprojective varieties

Marc Abboud
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Abstract

We define a local intersection number for metrised line bundles over quasiprojective varieties with compact support and show the local arithmetic Hodge index theorem for this intersection number. As a consequence we obtain a uniqueness result for the Monge-Amp\`ere equation over quasiprojective varieties within a certain class of solutions both in the archimedean and non-archimedean setting.

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Marc Abboud. 2025-03-18. A local version of the arithmetic Hodge index theorem over quasiprojective varieties. https://arxiv.org/abs/2503.14099

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