Essential dimension of spinor and Clifford groups

Chernousov, Vladimir; Merkurjev, Alexander

doi:10.2140/ant.2014.8.457

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Essential dimension of spinor and Clifford groups

Vladimir Chernousov and Alexander Merkurjev

Vol. 8 (2014), No. 2, 457–472

DOI: 10.2140/ant.2014.8.457

Abstract

We conclude the computation of the essential dimension of split spinor groups, and an application to algebraic theory of quadratic forms is given. We also compute essential dimension of the split even Clifford group or, equivalently, of the class of quadratic forms with trivial discriminant and Clifford invariant.

Keywords

Linear algebraic groups, spinor groups, essential dimension, torsor, nonabelian cohomology, quadratic forms, Witt rings, the fundamental ideal

Mathematical Subject Classification 2010

Primary: 11E04, 11E57, 11E72

Secondary: 11E81, 14L35, 20G15

Milestones

Received: 27 March 2013

Revised: 25 May 2013

Accepted: 24 June 2013

Published: 18 May 2014

Authors

Vladimir Chernousov
Department of Mathematical Sciences University of Alberta Edmonton, AB T6G 2G1 Canada

Alexander Merkurjev
Department of Mathematics University of California, Los Angeles Los Angeles, CA 90095-1555 United States

Vol. 8, No. 2, 2014