Duality invariance of Faltings heights, Hodge line bundles and global periods
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915522808905728 |
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| author | Suzuki, Takashi |
| author_facet | Suzuki, Takashi |
| contents | We prove that an abelian variety and its dual over a global field have the same Faltings height and, more precisely, have isomorphic Hodge line bundles, including their natural metrized bundle structures. More carefully treating real places, we also show that these abelian varieties have the same real and global periods that appear in the Birch-Swinnerton-Dyer conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04993 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Duality invariance of Faltings heights, Hodge line bundles and global periods Suzuki, Takashi Number Theory Algebraic Geometry 11G10 (Primary) 11G50, 11R58, 14G20, 14G25 (Secondary) We prove that an abelian variety and its dual over a global field have the same Faltings height and, more precisely, have isomorphic Hodge line bundles, including their natural metrized bundle structures. More carefully treating real places, we also show that these abelian varieties have the same real and global periods that appear in the Birch-Swinnerton-Dyer conjecture. |
| title | Duality invariance of Faltings heights, Hodge line bundles and global periods |
| topic | Number Theory Algebraic Geometry 11G10 (Primary) 11G50, 11R58, 14G20, 14G25 (Secondary) |
| url | https://arxiv.org/abs/2504.04993 |