Vol. 3, No. 4, 2009

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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
Abstract

Let p be a prime, k a field of characteristic p and N the normalizer of the maximal torus in the projective linear group PGLn. We compute the exact value of the essential dimension edk(N;p) of N at p for every n 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