On the Brauer group of the product of a torus and a semisimple algebraic group

الأصل · EN

Let T be a torus (not assumed to be split) over a field F, and denote by ₙH²et(X,Gm) the subgroup of elements of exponent dividing n in the cohomological Brauer group of a scheme X over the field F. We provide conditions on X and n for which the pull-back homomorphism ₙH²et(T,Gm)→ₙH²et(X× T,Gm) is an isomorphism. We apply this to compute the Brauer group of some reductive groups and of non singular affine quadrics. Apart from this, we investigate the p-torsion of the Azumaya algebra defined Brauer group of a regular affine scheme over a field F of characteristic p>0.