A local version of the arithmetic Hodge index theorem over quasiprojective varieties
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915252956823552 |
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| author | Abboud, Marc |
| author_facet | Abboud, Marc |
| contents | 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-Ampère equation over quasiprojective varieties within a certain class of solutions both in the archimedean and non-archimedean setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A local version of the arithmetic Hodge index theorem over quasiprojective varieties Abboud, Marc Algebraic Geometry Number Theory 14G40, 32P05, 32W20 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-Ampère equation over quasiprojective varieties within a certain class of solutions both in the archimedean and non-archimedean setting. |
| title | A local version of the arithmetic Hodge index theorem over quasiprojective varieties |
| topic | Algebraic Geometry Number Theory 14G40, 32P05, 32W20 |
| url | https://arxiv.org/abs/2503.14099 |