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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 145, Issue 2
  • September 2008, pp. 295-303

Cohomological invariants of odd degree Jordan algebras

  • MARK L. MacDONALD (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004108001485
  • Published online: 01 September 2008
Abstract
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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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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