Mathematical Sciences: Constraints on Galois Representationswith Applications

数学科学：伽罗瓦表示的约束及其应用

• 批准号: 9014522
• 负责人: Nigel Boston
• 金额: $ 3.81万
• 依托单位: University of Illinois at Urbana-Champaign
• 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: 1991-03-01 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9014522&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Constraints; Galois; Representationswith

Professor Boston will work on classifying p-adic representations of Galois groups. He hopes to show that in certain cases the deformation space defined by certain mod p representations is empty. This in turn would imply the non- existence of certain elliptic curves. 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 conse- quences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

波士顿教授将致力于将p-adic 伽罗瓦群的表示 他希望通过 在某些情况下，变形空间由特定的模p定义， 表示为空。 这反过来又意味着， 某些椭圆曲线的存在性 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 证明是非常富有成效的-最近解决了 几代人都面临的问题。 在众多的conse中， 序列是新的纠错码。 这些代码是 对于现代计算机（硬盘）和紧凑型 磁盘。