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

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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 $(\mathbb {Q}/\mathbb {Z})’(2)$ 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.## References

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## Additional Information

**Skip Garibaldi**- Affiliation: Department of Mathematics & Computer Science, Emory University, Atlanta, Georgia 30322
- MR Author ID: 622970
- ORCID: 0000-0001-8924-5933
- Email: skip@member.ams.org
- Received by editor(s): August 15, 2003
- Received by editor(s) in revised form: March 21, 2004
- Published electronically: March 31, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**358**(2006), 359-371 - MSC (2000): Primary 11E76; Secondary 17B25, 20G10
- DOI: https://doi.org/10.1090/S0002-9947-05-03676-7
- MathSciNet review: 2171237