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Spinors and essential dimension

Part of: Linear algebraic groups and related topics Forms and linear algebraic groups

Published online by Cambridge University Press:  02 March 2017

Skip Garibaldi  and
Robert M. Guralnick
Skip Garibaldi
Affiliation:
Center for Communications Research, San Diego, CA 92121, USA email skip@member.ams.org
Robert M. Guralnick
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA email guralnic@usc.edu
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Abstract

We prove that spin groups act generically freely on various spinor modules, in the sense of group schemes and in a way that does not depend on the characteristic of the base field. As a consequence, we extend the surprising calculation of the essential dimension of spin groups and half-spin groups in characteristic zero by Brosnan et al. [Essential dimension, spinor groups, and quadratic forms, Ann. of Math. (2) 171 (2010), 533–544], and Chernousov and Merkurjev [Essential dimension of spinor and Clifford groups, Algebra Number Theory 8 (2014), 457–472] to fields of characteristic different from two. We also complete the determination of generic stabilizers in spin and half-spin groups of low rank.

Keywords

spin modulespin groupcharacteristic 2essential dimensiongenerically freehalf-spin representation

MSC classification

Primary: 11E72: Galois cohomology of linear algebraic groups
Secondary: 11E88: Quadratic spaces; Clifford algebras 20G10: Cohomology theory
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 3 , March 2017 , pp. 535 - 556
Copyright
© The Authors 2017 

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