Mathematical Sciences: K-Theory of Fields

本课题涉及场的k理论。首席研究员将尝试扩展Rost和Merkerjev-Suslin的结果。他将使用相对k理论的技术来提供对场的权重三k理论的理解。他还将利用他最近构建的相对米尔诺k群来构建动机复合体。本研究涉及代数k理论。从广义上讲，代数k理论涉及线性代数概念的演变，如基和向量空间。这项工作对数论和代数几何具有重要意义，并有望在数学的许多不同领域之间建立令人兴奋的联系。

This project is concerned with the K-theory of fields. The principal investigator will attempt to extend the results of Rost and Merkerjev-Suslin. He will employ the techniques of relative K-theory to provide an understanding of the weight three K-theory of fields. He will also employ his recently constructed relative Milnor K-groups to construct motivic complexes. 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.