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

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Abstract

Let T be a torus (not assumed to be split) over a field F, and denote by nH 2et (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 2et (T,{ie375-2}) → n H 2et (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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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada

    Stefan Gille

  2. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    Nikita Semenov

Authors
  1. Stefan Gille
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  2. Nikita Semenov
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Correspondence to Stefan Gille.

Additional information

The work of the first-named author has been supported by an NSERC research grant. The authors acknowledge a partial support of SFB/Transregio 45 “Periods, moduli spaces and arithmetic of algebraic varieties”.

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Gille, S., Semenov, N. On the Brauer group of the product of a torus and a semisimple algebraic group. Isr. J. Math. 202, 375–403 (2014). https://doi.org/10.1007/s11856-014-1087-y

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  • DOI: https://doi.org/10.1007/s11856-014-1087-y

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