A local version of the arithmetic Hodge index theorem over quasiprojective varieties
Algebraic Geometry
2025-04-23 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.2503.14099,
title = {A local version of the arithmetic Hodge index theorem over quasiprojective varieties},
author = {Marc Abboud},
journal= {arXiv preprint arXiv:2503.14099},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2406.11510