Mathematical Sciences: On Azumaya Algebras of Order Two

拟议的研究涉及的理论， 交换环上的Azumaya代数。 校长 研究者将检查是否存在以下情况： 某些交换环的2-扭Brauer群。 工作 利用表面的坐标环，该项目将尝试 从几何学的角度来衡量这个演示的失败 的表面。 这项研究是在代数的一般领域，是一个 代数、数论和代数的有趣结合 几何 给定一个表面，可以将它与一个 一个坐标环和一个群。 该项目将 检查该组的属性，以确定 表面的几何形状。

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.