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

这个项目是关于特征不同于二的域上二次型的代数理论。主要研究人员将利用不同Galois模中系数的Galois上同调来研究Witt环中的无挠性质。他还将研究定义在任意域上的椭圆曲线上的二次型。特别是，他将使用etale上同调来研究这种形式的Witt环，特别是当定义在局部域上时。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 different from two. The principal investigator will investigate torsion-free properties in the Witt ring using Galois cohomology with coefficients in various Galois modules. He will also study quadratic forms over elliptic curves defined over an arbitrary field. In particular, he will use etale cohomology to investigate the Witt ring of such forms, especially when defined over a local field. 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 symmetric inner products on vector spaces over these fields. Thus the forms are intimately connected to the geometry of the space.