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Cohomological invariants of odd degree Jordan algebras

Published online by Cambridge University Press:  01 September 2008

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

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 2 , September 2008 , pp. 295 - 303
Copyright
Copyright © Cambridge Philosophical Society 2008

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