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

这个奖项支持在不同于2的特征域上的二次型代数理论的研究，以及在这些域上的适当格式，特别是具有有理点的完全规则曲线上的研究。特别是，主要研究者将研究对称双线性空间上的一个方案和他们的等价类在维特环利用几何和ettale方法。他还将研究具有2进系数的伽罗瓦上同调及其与二次型理论问题的关系。所支持的研究涉及二次型理论。它最简单的形式，是对二阶多项式形式的研究。等价地，它是对可以定义n维向量空间度量几何的内积类型的分析。二次型的研究与代数几何和代数k理论有着密切的联系。

This award supports investigations into the algebraic theory of quadratic forms over fields of characteristic different from two and over schemes proper over such fields, especially complete regular curves with a rational point. In particular, the principal investigator will investigate symmetric bilinear spaces over a scheme and their equivalence classes in the Witt ring utilizing geometric and etale methods. He will also study Galois cohomology with 2-adic coefficients and its relationship to quadratic form theoretic questions. The research supported involves the theory of quadratic forms. This, in its simplest form, is the study of polynomial forms of degree two. Equivalently, it is an analysis of the types of inner products that can define the metric geometry of an n-dimensional vector space. The study of quadratic forms has deep interrelations with algebraic geometry and algebraic k-theory.