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arXiv · 1812.03619

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

Thomas H. Geisser·Takashi Suzuki
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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.

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Thomas H. Geisser, Takashi Suzuki. 2019-09-18. A Weil-etale version of the Birch and Swinnerton-Dyer formula over function fields. https://doi.org/10.1016/j.jnt.2019.08.013

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