Special values of L-functions of one-motives over function fields
Number Theory
2022-11-28 v3 Algebraic Geometry
Abstract
The purpose of this paper is to give a formula for the leading coefficient at of the -function of one-motives over function fields in terms of Weil-\'etale cohomology, generalizing the Weil-\'etale 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-Oesterl\'e in terms of Weil-\'etale cohomology, and reprove their Tamagawa number formula.
Keywords
Cite
@article{arxiv.2009.14504,
title = {Special values of L-functions of one-motives over function fields},
author = {Thomas H. Geisser and Takashi Suzuki},
journal= {arXiv preprint arXiv:2009.14504},
year = {2022}
}
Comments
Accepted for publication in Journal f\"ur die reine und angewandte Mathematik. 26 pages