Spinors and essential dimension. (2nd March 2017)

• Record Type: Journal Article
• Authors: Garibaldi, Skip; Guralnick, Robert M.
• Is Part Of: Compositio mathematica. Volume 153:Number 3(2017)
• Page Start: 535
• Page End: 556
• Publication Date: 2017-03-02
• Subjects: 11E72 (primary), -- 11E88, -- 20G10 (secondary); spin module, -- spin group, -- characteristic 2, -- essential dimension, -- generically free, -- half-spin representation; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16008162
• Languages: English
• ISSNs: 0010-437X

Abstract

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 Theory8 (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.