Degree 3 unramified cohomology of classifying spaces for exceptional groups

Abstract

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 G(2), F-4, E-6, E-7, E-8. 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. (C) 2021 Elsevier B.V. All rights reserved.