Unramified cohomology of classifying varieties for exceptional simply connected groups

Details Unramified cohomology of classifying varieties for exceptional simply connected groups Unramified cohomology of classifying varieties for exceptional simply connected groups

2003-04-18

arxiv.org/abs/math/0304270v1

Transactions of the American Mathematical Society 358 #1 (2006) 359-371

Mathematics

Algebraic Geometry

Scientific paper

10.1090/S0002-9947-05-03676-7

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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