Spinors and essential dimension. (2nd March 2017) - Garibaldi, Skip; Guralnick, Robert M.
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.