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

被引：3
|
作者：
Geisser, Thomas H. [1 ]
Suzuki, Takashi [2 ]
机构：
[1] Rikkyo Univ, Dept Math, 3-34-1 Nishiikebukuro, Toshima City, Tokyo 1718501, Japan
[2] Chuo Univ, Dept Math, Bunkyo Ku, 1-13-27 Kasuga, Tokyo 1128551, Japan
来源：
JOURNAL OF NUMBER THEORY | 2020年 / 208卷
关键词：
Birch and Swinnerton-Dyer conjecture; Global function fields; Weil-etale cohomology; CONJECTURE;
D O I：
10.1016/j.jnt.2019.08.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (C) 2019 Elsevier Inc. All rights reserved.
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页码：367 / 389
页数：23
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