Algebraic K-Theory and Algebraic Groups

代数 K 理论和代数群

• 批准号: 9801646
• 负责人: Alexander Merkurjev
• 金额: $ 14.02万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-06-01 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801646&HistoricalAwards=false
• 关键词: Algebraic; Theory; Groups

ABSTRACT Alexander Merkurjev University of California, Los Angeles 98 01646 This project involves algebraic K-theory of algebraic varieties and the theory of algebraic groups. Professor Merkurjev intends to compute the K-groups of algebraic varieties with large automorphism group. As an application of this certain K-cohomology groups, such as Chow groups, will be computed. The investigator will also develop a theory of cohomological invariants of algebraic varieties and compute the group of cohomological invariants with coefficients in a given module. A powerful method in the modern mathematics is to study an object by studying its symmetries. Mathematicians have developed rather sophisticated ways of measuring symmetry, and they use a mathematical object called a group to keep track of them. Very often the groups can be stacked into a tower of increasingly complicated symmetries. By looking at the tower, they can get a great deal of information about the basic object. Algebraic K-theory is a version of this method of grouping. Professor Merkurjev has new ideas about how to compute these towers for certain kinds of objects. He hopes to use these computations to study algebraic varieties and algebraic groups. These are the mathematical names for a collection of solutions to a set of equations and for particular collections of matrices. The results of this project will add to our understanding of many basic pieces of mathematics.

摘要亚历山大·默克里耶夫（Alexander Merkurjev）加利福尼亚大学，洛杉矶98 01646该项目涉及代数的代数K理论和代数群体的理论。 Merkurjev教授打算将代数品种的K组与大型自动形态群体进行。 作为某些K-合理学组（例如Chow组）的应用。 研究者还将开发一个代数品种的共生理论理论，并在给定模块中使用系数计算具有系数的共同体学不变性。 现代数学中的一种强大方法是通过研究其对称性来研究对象。 数学家已经开发了测量对称性的相当复杂的方法，他们使用称为组的数学对象来跟踪它们。通常，这些群体可以堆叠在越来越复杂的对称性的塔中。通过查看塔，他们可以获得有关基本对象的大量信息。代数K理论是这种分组方法的一种版本。 Merkurjev教授有关于如何计算某些物体这些塔的新想法。 他希望使用这些计算来研究代数品种和代数组。 这些是用于一组方程和特定矩阵集合的解决方案集合的数学名称。 该项目的结果将增加我们对许多基本数学部分的理解。