Unramified cohomology of classifying varieties for exceptional simply connected groups

Garibaldi, Skip

doi:10.1090/S0002-9947-05-03676-7

Unramified cohomology of classifying varieties for exceptional simply connected groups
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Trans. Amer. Math. Soc. 358 (2006), 359-371 Request permission

Abstract:

Let $BG$ be a classifying variety for an exceptional simple simply connected algebraic group $G$. We compute the degree 3 unramified Galois cohomology of $BG$ with values in $(\mathbb {Q}/\mathbb {Z})’(2)$ over an arbitrary field $F$. Combined with a paper by Merkurjev, this completes the computation of these cohomology groups for $G$ semisimple simply connected over all fields. These computations provide another family of examples of simple simply connected groups $G$ such that $BG$ is not stably rational.

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