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

Stefan Gille, Nikita Semenov

Let T be a torus (not assumed to be split) over a field F, and denote by ${}_n{H}_{et}^2(X,Gm)$ the subgroup of elements of exponent dividing n in the cohomological Brauer group of…