Mathematical Sciences: Galois Representations Occurring in Mordell-Weil Groups

数学科学：Mordell-Weil 群中出现的伽罗瓦表示

• 批准号: 9114603
• 负责人: David Rohrlich
• 金额: --
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-11-01 至 1992-07-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9114603&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Galois; Representations; Occurring

Professor Rohrlich will work on several problems connected with the realization of Galois representations of Mordell-Weil groups of elliptic curves. In particular, whether certain irreducible Artin representations occur and if so what are their multiplicities. 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.

Rohrlich 教授将研究与实现椭圆曲线 Mordell-Weil 群的伽罗瓦表示相关的几个问题。 特别是，是否存在某些不可约的 Artin 表示，如果存在，它们的多重性是什么。 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。