Mathematical Sciences: Quadratic Forms and Galois Cohomology

在二次型理论的现代发展中， 最重要的问题一直是 不变量 用维特环的语言来说，这就是问题所在 从不同的部分或子元素中找到同态 将维特环转化为其他更容易处理代数环， 实体. 该项目研究了一个重要的 这个问题的子问题称为Arason-Milnor问题。 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，研究空间几何 具有对称的内积。 项目概述 所涉领域的一些最重要问题， 代数二次型

In the modern development of quadratic form theory, one of the most important problems has always been that of finding invariants. In the language of Witt rings, this is the problem of finding homomorphisms from various parts or subquotients of the Witt ring into other, hopefully more manageable, algebraic entities. This project studies several aspects of an important subproblem of this problem called the Arason-Milnor problem. 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 algebraic quadratic forms.