Mathematical Sciences: On the Brauer Group of a Variety

这个项目涉及代数问题 关于簇上的Azumaya代数的理论。 如果 X是代数闭域k上的簇， Azumaya X-代数参数化到Brauer等价 Brauer群B（X）。 主要研究者将 用代数上同调方法研究B（X） 几何 然后他会利用这些属性来获得 关于变量X的几何信息。 这项研究是在代数的一般领域， 一个有趣的结合环理论，数论和 代数几何 给定一个表面， 与它相关联的是一个坐标环， 组，以确定曲面的几何形状。

This project deals with questions in algebra concerning the theory of Azumaya algebras on a variety. If X is a variety over an algebraically closed field k, the Azumaya X-algebras are parametrized up to Brauer equivalence by the Brauer group B(X). The principal investigator will study B(X) using cohomological techniques from algebraic geometry. Then he will apply these properties to gain information about the geometry of the variety X. This research is in the general area of algebra and is an interesting combination of ring theory, number theory and algebraic geometry. Given a surface it is possible to associate with it a coordinate ring and with this ring a group in an effort to determine the geometry of the surface.