Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Cohomological invariants of odd degree Jordan algebras

MARK L. MacDONALDa1

a1 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB. e-mail: M.MacDonald@dpmms.cam.ac.uk

Abstract

In this paper we determine all possible cohomological invariants of Aut(J)-torsors in Galois cohomology with mod 2 coefficients (characteristic of the base field not 2), for J a split central simple Jordan algebra of odd degree n ≥ 3. This has already been done for J of orthogonal and exceptional type, and we extend these results to unitary and symplectic type. We will use our results to compute the essential dimensions of some groups, for example we show that ed(PSp2n) = n + 1 for n odd.

(Received August 20 2007)

(Revised October 22 2007)