The essential dimension of the normalizer of a maximal torus in the projective linear group

Meyer, Aurel; Reichstein, Zinovy

doi:10.2140/ant.2009.3.467

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The essential dimension of the normalizer of a maximal torus in the projective linear group

Aurel Meyer and Zinovy Reichstein

Vol. 3 (2009), No. 4, 467–487

DOI: 10.2140/ant.2009.3.467

Abstract

Let $p$ be a prime, $k$ a field of characteristic $\neq p$ and $N$ the normalizer of the maximal torus in the projective linear group ${PGL}_{n}$ . We compute the exact value of the essential dimension ${ed}_{k} (N; p)$ of $N$ at $p$ for every $n \geq 1$ .

Keywords

essential dimension, central simple algebra, character lattice, finite p-group, Galois cohomology

Mathematical Subject Classification 2000

Primary: 11E72

Secondary: 20D15, 16K20

Milestones

Received: 9 September 2008

Revised: 5 December 2008

Accepted: 19 December 2008

Published: 15 June 2009

Authors

Aurel Meyer
Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver, BC V6T 1Z2 Canada
http://www.math.ubc.ca/~aurel
Zinovy Reichstein
Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver, BC V6T 1Z2 Canada
http://www.math.ubc.ca/~reichst

Vol. 3, No. 4, 2009