Cohomological invariants of algebraic tori

被引：29

作者：

Blinstein, Sam ^{[1
]}

Merkurjev, Alexander ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

ALGEBRA & NUMBER THEORY | 2013年 / 7卷 / 07期

关键词：

algebraic tori; cohomological invariants; Galois cohomology; BRAUER GROUP; SPACES;

D O I：

10.2140/ant.2013.7.1643

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be an algebraic group over a field F. As defined by Serre, a cohomological invariant of G of degree n with values in Q = Z. j/is a functorial-in-K collection of maps of sets TorsG. K/F H-n. K; Q = Z. j/Ffor all field extensions K= F, where TorsG. K/is the set of isomorphism classes of G-torsors over Spec K. We study the group of degree 3 invariants of an algebraic torus with values in Q = Z.2/. In particular, we compute the group H-nr.(3) F(S) Q = Z.2//of unramified cohomology of an algebraic torus S.

引用

页码：1643 / 1684

页数：42