COMPARING THE BRAUER GROUP TO THE TATE-SHAFAREVICH GROUP

被引：6
作者：
Geisser, Thomas H. [1 ]
机构：
[1] Rikkyo Univ, Tokyo, Japan
来源：
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2020年 / 19卷 / 03期
基金：
日本学术振兴会;
关键词：
Brauer group; Tate-Shafarevich group; CURVES;
D O I：
10.1017/S1474748018000294
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a formula relating the order of the Brauer group of a surface fibered over a curve over a finite field to the order of the Tate-Shafarevich group of the Jacobian of the generic fiber. The formula implies that the Brauer group of a smooth and proper surface over a finite field is a square if it is finite.
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页码：965 / 970
页数：6
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