A lower bound on the essential dimension of simple algebras

Merkurjev, Alexander

doi:10.2140/ant.2010.4.1055

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A lower bound on the essential dimension of simple algebras

Alexander S. Merkurjev

Vol. 4 (2010), No. 8, 1055–1076

DOI: 10.2140/ant.2010.4.1055

Abstract

Let $p$ be a prime integer and $F$ a field of characteristic different from $p$ . We prove that the essential $p$ -dimension ed $_{p} (C S A (p^{r}))$ of the class $C S A (p^{r})$ of central simple algebras of degree $p^{r}$ is at least $(r - 1) p^{r} + 1$ . The integer ${ed}_{p} (C S A (p^{r}))$ measures complexity of the class of central simple algebras of degree $p^{r}$ 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

Vol. 4, No. 8, 2010