The conjectures of Artin-Tate and Birch-Swinnerton-Dyer
| Autor: | Lichtenbaum, S., Ramachandran, N., Suzuki, T. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Ãpijournal de Géométrie Algébrique, Volume 6 (March 28, 2022) epiga:7482 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.46298/epiga.2022.7482 |
| Popis: | 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. Comment: 18 pages, final version |
| Databáze: | arXiv |
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