Vol. 7, No. 7, 2013

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Cohomological invariants of algebraic tori

Sam Blinstein and Alexander Merkurjev

Vol. 7 (2013), No. 7, 1643–1684
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.

Keywords
algebraic tori, cohomological invariants, Galois cohomology
Mathematical Subject Classification 2010
Primary: 11E72
Secondary: 12G05
Milestones
Received: 23 April 2012
Revised: 8 October 2012
Accepted: 9 November 2012
Published: 12 October 2013
Authors
Sam Blinstein
Department of Mathematics
University of California, Los Angeles
Los Angeles CA 90095-1555
United States
Alexander Merkurjev
Department of Mathematics
University of California, Los Angeles
Los Angeles CA 90095-1555
United States