On the Brauer group of an algebraic group

Abstract: In the first part of my talk I will present a proof that if F is a field of characteristic 0 and G is a (connected) simply connected semisimple algebraic group over F then the natural homomorphism Br(F)Br(G) is an isomorphism. In the second part I will show that this fails in positive characteristic. More precisely, if G is a linear algebraic group of (Krull-)dimension bigger or equal 2 over a field F of positive characteristic then the natural split monomorphism Br(F)Br(G) is not surjective.