Brauer groups of linear algebraic groups with characters

Abstract

Let G be a connected linear algebraic group over an algebraically closed field of characteristic zero. Then the Brauer group of G is shown to be C × ( Q / Z ) ( n ) C \times {({\mathbf {Q}}/Z)^{(n)}} where C is finite and n = d ( d − 1 ) / 2 n = d(d - 1)/2 , with d the Z-rank of the character group of G. In particular, a linear torus of dimension d has Brauer group ( Q / Z ) ( n ) {({\mathbf {Q}}/Z)^{(n)}} with n as above.