The conjectures of Artin-Tate and Birch-Swinnerton-Dyer

S. Lichtenbaum; N. Ramachandran; T. Suzuki

doi:10.46298/epiga.2022.7482

S. Lichtenbaum ; N. Ramachandran ; T. Suzuki - The conjectures of Artin-Tate and Birch-Swinnerton-Dyer

epiga:7482 - Épijournal de Géométrie Algébrique, March 28, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.7482

The conjectures of Artin-Tate and Birch-Swinnerton-DyerArticle

Authors: S. Lichtenbaum ; N. Ramachandran ; T. Suzuki

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

https://doi.org/10.46298/epiga.2022.7482

Source: arXiv.org:2101.10222

Volume: Volume 6

Published on: March 28, 2022

Accepted on: March 28, 2022

Submitted on: May 14, 2021

Keywords: Mathematics - Algebraic Geometry

Licence: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)