On the order three Brauer classes for cubic surfaces

被引：6

作者：

Elsenhans, Andreas-Stephan ^{[1
]}

Jahnel, Joerg ^{[2
]}

机构：

[1] Univ Bayreuth, Math Inst, D-95440 Bayreuth, Germany

[2] Univ Siegen, Dept Math, D-57068 Siegen, Germany

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2012年 / 10卷 / 03期

关键词：

Cubic surface; Steiner trihedron; Triplet; Twisted cubic curve; Weak approximation; Explicit Brauer-Manin obstruction;

D O I：

10.2478/s11533-012-0042-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over Q such that Br(S)/Br(Q) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.

引用

页码：903 / 926

页数：24

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