Mathematical Sciences: Algebraic Geometry and Motivic Cohomology

数学科学：代数几何和动机上同调

• 批准号: 8902720
• 负责人: Spencer Bloch
• 金额: $ 17.15万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902720&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Geometry; Motivic

Professor Bloch will be working on Motives in algebraic geometry, and their cohomology. He has introduced a complex of higher algebraic cycles for the purpose of calculating the extension groups in the abelian category of "mixed" motives, and plans to study this complex and how it may be employed as a vehicle for realizing the category of mixed motives as a subcategory of the derived category of abelian groups. This is research in the field of Algebraic Geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origins, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from Algebra, but from Analysis and Topology, and conversely is finding application in those fields as well as in theoretical Computer Science and in Robotics.

布洛赫教授将研究代数几何中的动机及其上同调。为了计算“混合”动机的阿贝尔范畴的可拓群，他引入了一个高代数循环复合体，并计划研究这个复合体，以及如何利用它作为载体来实现混合动机范畴作为阿贝尔群派生范畴的子范畴。这是代数几何领域的研究，代数几何是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，并且反过来在这些领域以及理论计算机科学和机器人技术中得到应用。