Mathematical Sciences: Algebraic K-Theory and Motivic Cohomology

数学科学：代数 K 理论和动机上同调

• 批准号: 9501242
• 负责人: Andrei Suslin
• 金额: $ 16.83万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501242&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Theory; Motivic

This award supports the study of motivic cohomology of schemes and its relationships to algebraic K-theory. Recent developments concerning a spectral sequence relating algebraic K-theory to higher Chow groups and the computation of the higher Chow groups of complex varieties of sufficiently high codimension in terms of etale cohomology give a complete understanding of algebraic K-theory with finite coefficients of smooth complex varieties of dimension less than or equal to 2. The principal investigator will pursue further this line of investigation in order to obtain an understanding of algebraic K-theory of higher dimensional complex varieties and of more general schemes. In addition to this study of motivic cohomology, he will investigate the relationship between polyrelative algebraic K-theory and cyclic homology, thus completing a series of works on excision in algebraic K-theory. 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.

该奖项支持研究动机上同调的计划及其关系代数K理论。 最近的事态发展有关的频谱序列有关代数K-理论的高周群和计算高周群的复杂品种的足够高的余维的etale上同调给一个完整的理解代数K-理论有限系数光滑复杂品种的维数小于或等于2。 首席研究员将进一步追求这条线的调查，以获得理解代数K理论的高维复杂的品种和更一般的计划。 除了这个研究motivic上同调，他将调查之间的关系polyrelative代数K-理论和循环的同源性，从而完成了一系列工作切除代数K-理论。 这是代数几何领域的研究，它是现代数学中最古老的部分之一，但在过去的四分之一世纪里，它已经有了革命性的发展。 在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。 如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，并且反过来在这些领域以及理论计算机科学和机器人学中找到应用。