On the Brauer group of the product of a torus and a semisimple algebraic group |
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Authors: | Stefan Gille Nikita Semenov |
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Institution: | 1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada 2. Institut für Mathematik, Johannes Gutenberg-Universit?t Mainz, Staudingerweg 9, 55099, Mainz, Germany
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Abstract: | Let T be a torus (not assumed to be split) over a field F, and denote by nH et 2 (X,{ie375-1}) the subgroup of elements of the 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 nH et 2 (T,{ie375-2}) → n H et 2 (X × F T, {ie375-3}) 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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