Mathematical Sciences: On Azumaya Algebras of Order Two

本文的研究内容是交换环上的Azumaya代数理论。主要研究人员将研究某些交换环的2-扭转Brauer群的表示的可能性。使用曲面的坐标环，该项目将尝试从曲面的几何形状来衡量此演示文稿的失败。这项研究属于代数的一般领域，是代数、数论和代数几何的有趣结合。给定一个曲面，就有可能把它和一个坐标环联系在一起，并把这个环和一个群联系起来。本项目将检查这一组的属性，以努力确定曲面的几何形状。

The proposed research is concerned with the theory of Azumaya algebras over a commutative ring. The principal investigator will examine the possibility of a presentation of the 2-torsion Brauer group of certain commutative rings. Working with the coordinate rings of surfaces, the project will try to measure the failure of this presentation in terms of the geometry of the surface. 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.