Cohomological and geometric approaches to rationality problems

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Unramified Brauer groups of finite and infinite groups (2012, background): “Subsequently, Bogo-molov, Maciel, and Petrov [3] showed that B 0 ( G ) = 0 when G is a ﬁnite simple group of Lie type A (cid:2) , whereas Kunyavski˘ı [17] recently proved that B 0 ( G ) = 0 for every quasisimple or almost simple group G .”