Cohomological invariants of odd degree Jordan algebras

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 ty...

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Published inMathematical proceedings of the Cambridge Philosophical Society Vol. 145; no. 2; pp. 295 - 303
Main Author MacDONALD, MARK L.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2008
Subjects
Algebraic group theory
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Summary: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.
Bibliography:istex:B04955CCB46DFE8F7B34F72D5E896CA479E3C74C
PII:S0305004108001485
ark:/67375/6GQ-DW33X2RD-X
ArticleID:00148
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004108001485