Mathematical Sciences: Algebraic K-theory

本研究涉及代数K-理论， 特别是K理论的结构和可计算性， 有奇异点的变种首席研究员计划 研究最近发现的陈特征，包括主要特征和 第二，其中涉及K-理论循环同源，以及， 关于奇异投射簇的K-群的猜想 都是由K群环构成的特殊的K-理论 环也将研究着眼于结构的结果 例如K-正则性和负K-群的消失。 支持的研究是在代数K理论和 代数几何在这个项目中，首席研究员 将K理论技术应用于代数曲面，研究 当奇点出现时，K群中发生的结构变化 阐述

This research is concerned with algebraic K-theory, particularly the structure and computability of the K-theory of varieties with singularities. The principal investigator plans to study the recently discovered chern characters, both primary and secondary, which relate K-theory to cyclic homology, as well as, the conjecture that the K-groups of a singular projective variety are built up from the K-groups of rings. The K-theory of special rings will also be studied with an eye toward structural results such as K-regularity and vanishing of negative K-groups. The research supported is in algebraic K-theory and algebraic geometry. In this project, the principal investigator applies K-theoretic techniques to algebraic surfaces, studying the structural changes that occur in K-groups when singularities are introduced.