Mathematical Sciences: Topics in Iwasawa Theory

数学科学：岩泽理论专题

• 批准号: 9100238
• 负责人: John Jones
• 金额: $ 4.17万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100238&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Iwasawa; Theory

Professor Jones will work on the Iwasawa theory of elliptic curves. He intends to study problems related to Iwasawa L- functions of l-adic representations. He will also study equivariant cohomology with a view towards finding analogues of flat duality theorems. 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.

琼斯教授将研究岩泽椭圆曲线理论。 他打算研究与 l-adic 表示的 Iwasawa L-函数相关的问题。 他还将研究等变上同调，以寻找平坦对偶定理的类似物。 该项目属于算术几何的一般领域，该学科融合了两个最古老的数学领域：数论和几何。 事实证明，这种结合非常富有成效——最近解决了几代人都面临的问题。 其众多后果之一就是新的纠错码。 此类代码对于现代计算机（硬盘）和光盘都是必不可少的。