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.

引用

页码：965 / 970

页数：6

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