Mathematical Sciences: Galois Structures, Capacity Theory and Intersection Theory

数学科学：伽罗瓦结构、容量论和交集论

• 批准号: 9400748
• 负责人: Ted Chinburg
• 金额: $ 7.5万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400748&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Galois; Structures; Capacity

Professor Chinburg will work on Galois Module Structure for Schemes and the connection between capacity theory and intersection theory on varieties. In particular he will work on Euler characteristics using equivariant Riemann-Roch theorems. He will also work on limits of metrizied cycles in arbitrary codimension. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

钦伯格教授将致力于方案的伽罗瓦模结构以及容量理论和簇上的交集理论之间的联系。特别是，他将使用等变Riemann-Roch定理来研究欧拉特征。他还将研究任意余维的度量化圈的极限。这个项目属于算术几何的一般领域--一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机(硬盘)和光盘都是必不可少的。