Open Access
2013 Cohomological invariants of algebraic tori
Sam Blinstein, Alexander Merkurjev
Algebra Number Theory 7(7): 1643-1684 (2013). DOI: 10.2140/ant.2013.7.1643


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.


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Sam Blinstein. Alexander Merkurjev. "Cohomological invariants of algebraic tori." Algebra Number Theory 7 (7) 1643 - 1684, 2013.


Received: 23 April 2012; Revised: 8 October 2012; Accepted: 9 November 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1368.11034
MathSciNet: MR3117503
Digital Object Identifier: 10.2140/ant.2013.7.1643

Primary: 11E72
Secondary: 12G05

Keywords: algebraic tori , cohomological invariants , Galois cohomology

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 7 • 2013
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