Mathematical Sciences: Homological Questions in Commutative Algebra

数学科学：交换代数中的同调问题

• 批准号: 9204297
• 负责人: Paul Roberts
• 金额: $ 14.1万
• 依托单位: University of Utah
• 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=9204297&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homological; Questions; Commutative

This award is concerned with the study of certain invariants, known as local Chern characters, defined for modules over local rings. These invariants have been defined for bounded complexes of free modules. The principal investigator will study the contributions of individual matrices defined by these complexes. He will also consider questions concerning multiplicities and other ideal-theoretic properties. The results of these studies will be applied to homological conjectures and to related problems. 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.

这个奖项是关于局部环上的模的某些不变量的研究，这些不变量被称为局部Chern特征标。这些不变量已被定义为自由模的有界复形。首席研究员将研究由这些复合体定义的各个矩阵的贡献。他还将考虑有关多重性和其他理想理论性质的问题。这些研究的结果将应用于同调猜想和相关问题。这是对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25年里，它取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及理论计算机科学和机器人学中也找到了应用。