Unramified cohomology of classifying varieties for exceptional simply connected groups

@article{Garibaldi2005UnramifiedCO,
  title={Unramified cohomology of classifying varieties for exceptional simply connected groups},
  author={Ryan Skip Garibaldi},
  journal={Transactions of the American Mathematical Society},
  year={2005},
  volume={358},
  pages={359-371}
}
  • R. Garibaldi
  • Published 2005
  • Mathematics
  • Transactions of the American Mathematical Society
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 family of examples of simple simply connected groups G such that BG is not stably rational. 
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