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

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