Cohomological invariants of odd degree Jordan algebras

Details Cohomological invariants of odd degree Jordan algebras Cohomological invariants of odd degree Jordan algebras

2008-01-10

arxiv.org/abs/0801.1634v1

Mathematics

Rings and Algebras

12 pages, to appear in Mathematical Proceedings of the Cambridge Philosophical Society

Scientific paper

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(PSp(2n))=n+1 for n odd.

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