Unramified Brauer groups of finite simple groups of Lie type $A_{\ell}$

Bogomolov, Fedor; Maciel, Jorge; Petrov, Tihomir

Unramified Brauer groups of finite simple groups of Lie type $A_{\ell}$

Authors

Bogomolov, Fedor

Maciel, Jorge

Petrov, Tihomir

Description

We study the subgroup B_0(G) of H^2(G,Q/Z) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B_0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B_0(G) is trivial for finite simple groups of Lie type A_{\ell}.
15 pages