Vol. 8, No. 2, 2014

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Essential dimension of spinor and Clifford groups

Vladimir Chernousov and Alexander Merkurjev

Vol. 8 (2014), No. 2, 457–472
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