16/07/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building Paulo Lima-Filho, Texas A&M University
The bigger Brauer group, twisted algebraic K-theory and motives
In this talk we will first survey basic aspects of the Brauer group and Taylor's "bigger Brauer group" both in an algebraic and topological contexts. We then proceed to present the connection between these notions and twisted forms of K-theory. In the topological context, these forms of twisted K-theory have appeared in the work of Witten and in the study of orbifolds in mathematical physics. We relate the Brauer group of the real numbers with two distinct equivariant forms of K-theories and corresponding equivariant cohomology theories. Finally, using the formalism of motives and recent work of Voevodsky, we propose to develop analogous twisted forms of algebraic K-theory and motivic cohomology for schemes over a base scheme S. These theories should be indexed by the (bigger) Brauer group of S.
