Vol. 4, No. 8, 2010

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A lower bound on the essential dimension of simple algebras

Alexander S. Merkurjev

Vol. 4 (2010), No. 8, 1055–1076
Abstract

Let p be a prime integer and F a field of characteristic different from p. We prove that the essential p-dimension edpCSA(pr) of the class CSA(pr) of central simple algebras of degree pr is at least (r 1)pr + 1. The integer edpCSA(pr) measures complexity of the class of central simple algebras of degree pr over field extensions of F.

Keywords
essential dimension, Brauer group, algebraic tori
Mathematical Subject Classification 2000
Primary: 16K50
Secondary: 14L30, 20G15
Milestones
Received: 27 November 2009
Revised: 30 March 2010
Accepted: 15 May 2010
Published: 24 February 2011
Authors
Alexander S. Merkurjev
Department of Mathematics
University of California
Los Angeles, CA 90095-1555
United States