Mathematical Sciences: The Algebraic Theory of Quadratic Forms and Galois Cohomology

该项目涉及的是 二次型在特征域以外的域上。的 首席研究员将研究 分次Witt环与系数为的Galois上同调环 整数模2。它将表明，对于大类 所有这些分次环都重合。为了实现这一点， 发展了二次型的相关理论。 这个项目是关于二次型的理论 forms.二次型是几个多项式的函数， 二阶齐次的变量二次形式 在两个特征以外的领域中， 这些域上向量空间的对称内积。 因此，这些形式与建筑物的几何形状密切相关。 空间

This project is concerned with the algebraic theory of quadratic forms over fields of characteristic other than two. The principal investigator will study the relationship between the graded Witt ring and galois cohomology rings with coefficients in the integers modulo two. It will be shown that for large classes of fields all these graded rings coincide. To accomplish this, a relative theory of quadratic forms will be developed. This project is concerned with the theory of quadratic forms. A quadratic form is a polynomial function of several variables which is homogeneous of degree two. Quadratic forms over fields of characteristic other than two arise naturally from the symetric inner products on vector spaces over these fields. Thus, the forms are intimately connected to the geometry of the space.