Spinors and essential dimension
Group Theory
2019-02-20 v2 Representation Theory
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--Reichstein--Vistoli (Annals of Math., 2010) and Chernousov--Merkurjev (Algebra & Number Theory, 2014) to fields of characteristic different from 2.
Cite
@article{arxiv.1601.00590,
title = {Spinors and essential dimension},
author = {Skip Garibaldi and Robert M. Guralnick},
journal= {arXiv preprint arXiv:1601.00590},
year = {2019}
}
Comments
v2 adds an appendix by Alexander Premet on generic stabilizer in HSpin_16 in characteristic 2