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

2013/03/21 by Stefan Gille, Gille, Stefan, Nikita Semenov +1
Mathematics · #14F22 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1303.5344

openalex publication_date 2013/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a torus (not assumed to be split) over a field F, and denote by\n_nH²_et(X,Gm) the subgroup of elements of exponent dividing n in the\ncohomological Brauer group of a scheme X over the field F. We provide\nconditions on X and n for which the pull-back homomorphism\n_nH²_et(T,Gm)\→_nH²_et(X\× T,Gm) is an isomorphism. We apply\nthis to compute the Brauer group of some reductive groups and of non singular\naffine quadrics. Apart from this, we investigate the p-torsion of the Azumaya\nalgebra defined Brauer group of a regular affine scheme over a field F of\ncharacteristic p>0.\n

Related

• Brauer groups of abelian varieties over fields of finite characteristic
• Brauer groups and quotient stacks
• Boundedness of the p-primary torsion of the Brauer group of products of varieties
• Une formule pour le groupe de Brauer algébrique d'un torseur
• Computing the Cohomological Brauer Group of a Toric Variety