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arXiv · 2009.14504

Special values of L-functions of one-motives over function fields

Thomas H. Geisser·Takashi Suzuki
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Abstract

The purpose of this paper is to give a formula for the leading coefficient at $s=1$ of the $L$-function of one-motives over function fields in terms of Weil-étale cohomology, generalizing the Weil-étale version of the Birch and Swinnerton-Dyer conjecture in the authors' previous work. As a consequence we express the Tamagawa number of a torus introduced by Ono-Oesterlé in terms of Weil-étale cohomology, and reprove their Tamagawa number formula.

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Thomas H. Geisser, Takashi Suzuki. 2022-10-15. Special values of L-functions of one-motives over function fields. https://doi.org/10.1515/crelle-2022-0081

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