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Unramified cohomology of classifying varieties for exceptional simply connected groups

Author: Skip Garibaldi
Journal: Trans. Amer. Math. Soc. 358 (2006), 359-371
MSC (2000): Primary 11E76; Secondary 17B25, 20G10
Published electronically: March 31, 2005
MathSciNet review: 2171237
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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.

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Additional Information

Skip Garibaldi
Affiliation: Department of Mathematics & Computer Science, Emory University, Atlanta, Georgia 30322

Received by editor(s): August 15, 2003
Received by editor(s) in revised form: March 21, 2004
Published electronically: March 31, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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