Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

数学科学：算术几何和 K 理论主题

• 批准号: 9501500
• 负责人: Henri Gillet
• 金额: $ 19.03万
• 依托单位: University of Illinois at Chicago
• 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=9501500&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Arithmetic; Geometry

Professor Gillet will continue his work on Arekelov theory and algebraic K-theory. He wishes to study non-archimedean Arekelov theory. He also intends to study the connections between K-theory and motives in particular to use motives to construct a K-theory with compact support. 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.

吉莱教授将继续他的工作Arekelov理论和代数K理论。他希望研究非阿基米德的阿雷克洛夫理论。他还打算研究K-理论和动机之间的联系，特别是利用动机来构建一个具有紧支撑的K-理论。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。 事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 这种代码对于现代计算机（硬盘）和光盘都是必不可少的。