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

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.

18 pages, final version

Cited by in corpus (2)

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