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arXiv · 2101.10222

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

S. Lichtenbaum·N. Ramachandran·T. Suzuki
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Abstract

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.

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S. Lichtenbaum, N. Ramachandran, T. Suzuki. 2021-01-25. The conjectures of Artin-Tate and Birch-Swinnerton-Dyer. https://doi.org/10.46298/epiga.2022.7482

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