This project deals with questions on the theory of Azumaya algebras over the function field of an algebraic variety. Let K be the function field of the surface S and A a central division algebra over K. The principal investigator will study the algebra A by using cohomological techniques from algebraic geometry in order to understand the ramification divisor of A on S. The project relates properties of the Brauer group of K to the geometry of divisors on S and considers questions about the factorization of the Brauer class of A into symbols. This research is in the general area of algebra and is an interesting combination of algebra, number theory and algebraic geometry. Given a surface it is possible to associate with it a coordinate ring and with this ring a group. This project will examine properties of this group in an effort to determine the geometry of the surface.
