ON THE HASSE PRINCIPLE FOR CERTAIN QUARTIC HYPERSURFACES

被引：5
|
作者：
Quan, Nguyen Ngoc Dong [1 ]
机构：
[1] Univ Arizona, Dept Math, Tucson, AZ 85721 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 12期
关键词：
Azumaya algebras; Brauer groups; Brauer-Manin obstruction; Hasse principle; quartic hypersurfaces; VARIETIES; SURFACES; POINTS; CURVES;
D O I：
10.1090/S0002-9939-2011-10936-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that there are infinitely many non-isomorphic quartic curves which are counter-examples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these quartic curves have no points defined over number fields of odd degree. As a consequence, we show that there are infinitely many quartic hypersurfaces of arbitrary dimension violating the Hasse principle.
引用
收藏
页码：4293 / 4305
页数：13
相关论文
共 50 条
12345