Lower bounds for essential dimensions in characteristic $2$ via orthogonal representations

Antonio Babic and Vladimir Chernousov

Vol. 279 (2015), No. 1-2, 37–63

DOI: 10.2140/pjm.2015.279.37

Abstract

We give a lower bound for the essential dimension of a split simple algebraic group of “adjoint” type over a field of characteristic $2$. We also compute the essential dimension of orthogonal and special orthogonal groups in characteristic $2$.

Keywords

linear algebraic group, torsor, essential dimension, orthogonal representation, Killing form, quadratic form

Mathematical Subject Classification 2010

Primary: 11E04, 11E57, 11E72

Secondary: 11E81, 14L35, 20G15

Milestones

Received: 16 March 2015

Revised: 14 May 2015

Accepted: 14 May 2015

Published: 21 December 2015