Canonical local heights and Berkovich skeleta
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917677163872256 |
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| author | de Jong, Robin Shokrieh, Farbod |
| author_facet | de Jong, Robin Shokrieh, Farbod |
| contents | We discuss canonical local heights on abelian varieties over non-archimedean fields from the point of view of Berkovich analytic spaces. Our main result is a refinement of Néron's classical result relating canonical local heights with intersection multiplicities on the Néron model. We also revisit Tate's explicit formulas for Néron's canonical local heights on elliptic curves. Our results can be viewed as extensions of Tate's formulas to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical local heights and Berkovich skeleta de Jong, Robin Shokrieh, Farbod Number Theory Algebraic Geometry 11G10, 11G50, 14G40, 14K25, 14T25, 14G20, 14K05 We discuss canonical local heights on abelian varieties over non-archimedean fields from the point of view of Berkovich analytic spaces. Our main result is a refinement of Néron's classical result relating canonical local heights with intersection multiplicities on the Néron model. We also revisit Tate's explicit formulas for Néron's canonical local heights on elliptic curves. Our results can be viewed as extensions of Tate's formulas to higher dimensions. |
| title | Canonical local heights and Berkovich skeleta |
| topic | Number Theory Algebraic Geometry 11G10, 11G50, 14G40, 14K25, 14T25, 14G20, 14K05 |
| url | https://arxiv.org/abs/2405.17826 |