Mathematical Sciences: Motives and Algebraic Cycles

数学科学：动机和代数循环

• 批准号: 9205230
• 负责人: Spencer Bloch
• 金额: $ 22.34万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9205230&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Motives; Algebraic; Cycles

This award supports work on motives and algebraic cycles. One of the principal investigators will work on motivic cohomology; a non-archimedean generalization of the Riemann-Roch type theorem proved by Gillet and Soule; and a generalization of Iwasawa theory to cycles and motives. The other principal investigator will work on the existence of higher logarithms using families of certain linear configurations over the Grassmannians, as well as explore the relationship between the Grassmannian complex and the K-groups of the ground field. 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 robotics.

该奖项支持动机和代数循环方面的工作。其中一名主要研究人员将研究动机上同；由Gillet和Soule证明的Riemann-Roch型定理的非阿基米德推广；以及将岩泽理论推广到循环和动机。另一名首席研究员将利用格拉斯曼复体上某些线性构型的族来研究高对数的存在性，并探索格拉斯曼复体与地面场k群之间的关系。这是代数几何领域的研究，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，而且还使用分析和拓扑的方法，相反，它在这些领域以及理论计算机科学和机器人技术中也得到了应用。