Degree 3 unramified cohomology of classifying spaces for exceptional groups

Let G be a reductive group defined over an algebraically closed field of characteristic 0 such that the Dynkin diagram of G is the disjoint union of diagrams of types G2, F4, E6, E7, E8. We show that the degree 3 unramified cohomology of the classifying space of G is trivial. In particular, combined...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 225; no. 10; p. 106718
Main Author Baek, Sanghoon
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2021
Subjects
12G05
20G41
11E72
14M17
14L30
20G10
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Summary:Let G be a reductive group defined over an algebraically closed field of characteristic 0 such that the Dynkin diagram of G is the disjoint union of diagrams of types G2, F4, E6, E7, E8. We show that the degree 3 unramified cohomology of the classifying space of G is trivial. In particular, combined with articles by Merkurjev [11] and the author [1], this completes the computations of degree 3 unramified cohomology and reductive invariants for all split semisimple groups of a homogeneous Dynkin type.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2021.106718