Mathematical Sciences: Algebraic K-theory

该奖项支持代数k理论的研究，特别是关于具有奇点的变种k理论的结构和可计算性的研究。主要研究者将通过陈氏特征、切环痕迹和次陈氏特征来研究k理论、陈氏上同调和循环同调之间的关系。他还将研究k理论的Adams运算，着眼于动机上同调和负k群的消失猜想。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，如基空间和向量空间。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 award supports research in algebraic K-theory, particularly with regard to the structure and computability of the K-theory of varieties with singularities. The principal investigator will investigate the relationship between K-theory, etale cohomology and cyclic homology, via the etale chern character, the cyclotomic trace and secondary chern character. He also will study the Adams operations on K-theory, with an eye toward vanishing conjectures for motivic cohomology and negative K-groups. 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.