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Unramified cohomology of classifying varieties for exceptional simply connected groups

R. Skip Garibaldi
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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 Q/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 example of a simple simply connected group G such that BG is not stably rational.

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R. Skip Garibaldi. 2003-04-18. Unramified cohomology of classifying varieties for exceptional simply connected groups. https://doi.org/10.1090/s0002-9947-05-03676-7

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