The conjectures of Artin-Tate and Birch-Swinnerton-Dyer
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909607917518848 |
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| author | Lichtenbaum, S. Ramachandran, N. Suzuki, T. |
| author_facet | Lichtenbaum, S. Ramachandran, N. Suzuki, T. |
| contents | We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of the generic fibre. As a byproduct, we obtain a new proof of a theorem of Geisser relating the orders of the Brauer group and the Tate-Shafarevich group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_10222 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The conjectures of Artin-Tate and Birch-Swinnerton-Dyer Lichtenbaum, S. Ramachandran, N. Suzuki, T. Algebraic Geometry We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of the generic fibre. As a byproduct, we obtain a new proof of a theorem of Geisser relating the orders of the Brauer group and the Tate-Shafarevich group. |
| title | The conjectures of Artin-Tate and Birch-Swinnerton-Dyer |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2101.10222 |