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Unramified Brauer groups of finite simple groups of Lie type \(A_\ell\). (English) Zbl 1058.14031

The authors consider subgroups \(B_0(G)\) of \(H^2(G,\mathbb Q/\mathbb Z)\) whose elements have trivial restrictions to every abelian subgroup of \(G\). In this fashion, \(B_0(G)\) provides the simplest nontrivial obstruction to stable rationality of certain algebraic varieties. Moreover, they prove that \(B_0(G)\) is trivial for finite simple groups of Lie type, to which the last section of their paper is devoted.

MSC:

14F22 Brauer groups of schemes
20J05 Homological methods in group theory
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