Mathematical Sciences: Quadratic Forms, Division Algebras and Galois Cohomology

本课题研究了代数学中的几个问题， 二次型理论与结构 任意域上的有限维可除代数 这些问题的研究使用伽罗瓦理论的工具， 伽罗瓦上同调 本研究涉及二次型理论， 是研究齐次二次方程的解 多项式，或等价地，几何的研究， 具有对称内积的空间。项目 概述了一些最重要的问题， quadratic forms的缩写。

This project studies several problems in the algebraic theory of quadratic forms and the structure of finite-dimensional division algebras over arbitrary fields. These problems are studied using the tools of Galois theory and Galois cohomology. This research concerns the theory of quadratic forms which is a study of the solutions of homogeneous second degree polynomials, or equivalently, the study of the geometry of spaces possessing a symmetric inner product. The project outlined concerns some of the most important problems in the area of quadratic forms.