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

页码：4293 / 4305

页数：13

共 22 条

[1] The Magma algebra system .1. The user language [J].