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

这个项目是关于特征域上的二次型的代数理论。主要研究分次Witt环与系数为模2的整数的Galois上同调环之间的关系。我们将证明，对于大类的域，所有这些分次环都是重合的。为了实现这一点，将发展二次型的相关理论。这个项目是关于二次型理论的。二次型是多个变量的二次齐次多项式函数。特征域上的二次型是由特征域上的向量空间上的对称内积自然产生的。因此，这些形式与空间的几何形状紧密相连。

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.