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

Stefan Gille; Nikita Semenov

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arXiv · 1303.5344

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

Stefan Gille·Nikita Semenov

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Abstract

Let T be a torus (not assumed to be split) over a field F, and denote by $_n{H^{2}_{et}(X,Gm)}$ 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 $_n{H^2_{et}(T,Gm)}\to_n{H^2_{et}(X\times T,Gm)}$ 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.

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BibTeX RIS

Stefan Gille, Nikita Semenov. 2013-03-21. On the Brauer group of the product of a torus and a semisimple algebraic group. https://arxiv.org/abs/1303.5344

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