Algebra & Number Theory

Cohomological invariants of algebraic tori

Sam Blinstein and Alexander Merkurjev

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

algebraic tori cohomological invariants Galois cohomology


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.

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