Mathematical Sciences: K-Theory & Motivic Cohomology

数学科学：K 理论

• 批准号: 9401164
• 负责人: Marc Levine
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401164&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; & Motivic

Levine The principal investigator will continue his study of the motivic category and other related constructions. He will investigate the relationship between the integral motivic cohomology and Bloch's higher Chow groups, to construct a weight structure and a duality on the motivic category, and to relate the motivic Tate category with the motivic Lie algebra constructed by Bloch and Kriz. He plans to lift various constructions in Hodge theory to the motivic setting and to study mod n motivic cohomology. The principal investigator will also use some new ideas of Hoobler to attack Kato's conjecture and will give a construction of a candidate for weight two 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. ***

莱文作为首席研究者，将继续他对理据范畴和其他相关结构的研究。他将研究积分动机上同调与Bloch的高阶Chow群之间的关系，在Motivic范畴上构造权结构和对偶，并将Motivic Tate范畴与Bloch和Kriz构造的Motivic Lie代数联系起来。他计划将霍奇理论中的各种结构提升到理据背景下，并研究现代理据上同调。主要研究人员还将利用Hoobler的一些新思想来攻击Kato猜想，并将构造一个二重上同调的候选者。这项研究涉及到代数K-理论。从广义上讲，代数K-理论涉及基和向量空间等线性代数概念的演化。这项工作对数论和代数几何具有重大意义，并有望在数学的许多不同领域之间建立令人兴奋的联系。***