Essential dimension, spinor groups, and quadratic forms

Pages 533-544 from Volume 171 (2010), Issue 1 by Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli

Abstract

We prove that the essential dimension of the spinor group $\mathbf{Spin}_n$ grows exponentially with $n$ and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more complex, in high dimensions, than previously expected.

Keywords
, , , ,
Mathematical Subject Classification

Primary 2000: , ,

DOI
https://doi.org/http://doi.org/10.4007/annals.2010.171.533
MR
2630047
zbMATH
05712735
Milestones
Received: 13 February 2007
Revised: 17 January 2008
Accepted: 14 April 2008
Published online: 17 March 2010

Authors

Patrick Brosnan

University of British Columbia, Department of Mathematics, 1984 Mathematics Road, Vancouver, V6T1Z2, Canada Zinovy Reichstein

University of British Columbia, Department of Mathematics, 1984 Mathematics Road, Vancouver, V6T1Z2, Canada Angelo Vistoli

Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy