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.


    Volume: Volume 6
    Published on: March 28, 2022
    Accepted on: March 28, 2022
    Submitted on: May 14, 2021
    Keywords: Mathematics - Algebraic Geometry

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