Mathematical Sciences: Research in K-Theory

这项研究涉及三个项目， 代数K理论 第一个是延续以前的 关于约化群扭形式的K-理论的工作 方案，目标是计算部分K-上同调 这样的计划。 第二个项目是利用这个 计算的K-理论的群计划，以得到一个很好的 齐性空间的K-理论的描述 还原群及其扭曲形式 第三个项目 本文是对汉语中的几种动机构式的考察 上同调 本研究涉及代数K理论。 在 广义代数K理论关注的是 线性代数中的概念，如基和向量空间。 这项工作对数论和 代数几何，并承诺作出令人兴奋的连接 数学中的许多不同领域。

This research is concerned with three projects in algebraic K-theory. The first is a continuation of previous work on the K-theory of twisted forms of reductive group schemes, with the goal of computing a part of the K-cohomology of such schemes. The second project is to use this computation of the K-theory of group schemes to get a good description of the K-theory of homogeneous spaces for reductive groups, and their twisted forms. The third project is an investigation of some constructions in motivic cohomology. This research is concerned with algebraic K-theory. In a broad sense algebraic K-theory concerns the evolution of concepts from linear algebra such as basis and vector space. This work has significant implications for number theory and algebraic geometry, and promises to make exciting connections between a number of different areas in mathematics.