Topology Seminar: Benedict Williams

  • Date: 10/31/2012
  • Time: 15:00
Benedict Williams, University of Southern California

University of British Columbia


The Brauer Group and Obstruction Theory


The study of central simple algebras over a field is a venerable topic in ring theory. There is a generalization of central simple algebras to schemes in the ├ętale topology (in fact to arbitrary ringed sites) due to Grothendieck. The group of equivalence classes of Azumaya algebras over X is known as the Brauer group of X. By comparing the ├ętale topology on a smooth complex variety X with the classical topology, we are able to use results from classical obstruction theory in order to obstruct the existence of certain Azumaya algebras. After giving an introduction to Azumaya algebras and the Brauer group, we shall present one such result, which furnishes lower bounds on the ranks of Azumaya algebras on spaces of low cohomological dimension.

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Location: ESB 4127