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

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.

arXiv commentAccepted for publication in Journal für die reine und angewandte Mathematik. 26 pages

References in corpus (4)

• A Weil-etale version of the Birch and Swinnerton-Dyer formula over function fields
• Neron models of 1-motives and duality
• Special values of $L$-functions on regular arithmetic schemes of dimension $1$
• Weil-etale cohomology and special values of L-functions at zero

Cited by in corpus (2)

• Chai's conjectures on base change conductors
• Tori over number fields and special values at s=1