Algebra & Number Theory

Cohomological invariants of algebraic tori

Sam Blinstein and Alexander Merkurjev

Full-text: Open access

Abstract

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 (j) is a functorial-in-K collection of maps of sets TorsG(K)Hn(K,(j)) for all field extensions KF, 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 (2). In particular, we compute the group Hnr3(F(S),(2)) of unramified cohomology of an algebraic torus S.

Article information

Source
Algebra Number Theory, Volume 7, Number 7 (2013), 1643-1684.

Dates
Received: 23 April 2012
Revised: 8 October 2012
Accepted: 9 November 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730053

Digital Object Identifier
doi:10.2140/ant.2013.7.1643

Mathematical Reviews number (MathSciNet)
MR3117503

Zentralblatt MATH identifier
1368.11034

Subjects
Primary: 11E72: Galois cohomology of linear algebraic groups [See also 20G10]
Secondary: 12G05: Galois cohomology [See also 14F22, 16Hxx, 16K50]

Keywords
algebraic tori cohomological invariants Galois cohomology

Citation

Blinstein, Sam; Merkurjev, Alexander. Cohomological invariants of algebraic tori. Algebra Number Theory 7 (2013), no. 7, 1643--1684. doi:10.2140/ant.2013.7.1643. https://projecteuclid.org/euclid.ant/1513730053


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