A Weil-etale version of the Birch and Swinnerton-Dyer formula over function fields

Abstract

We give a reformulation of the Birch and Swinnerton-Dyer conjecture over global function fields in terms of Weil-etale cohomology of the curve with coefficients in the Neron model, and show that it holds under the assumption of finiteness of the Tate-Shafarevich group.

Accepted for publication in the Journal of Number Theory. 23 pages

References in corpus (1)

• Duality for cohomology of curves with coefficients in abelian varieties

Cited by in corpus (4)

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• On $\mu$-invariants and isogenies for abelian varieties over function fields
• An improvement of the duality formalism of the rational etale site