Mathematical Sciences: Arthmetic of Elliptic Curves and Automorphic Forms over Function Fields

数学科学：椭圆曲线和函数域自守形式的算术

• 批准号: 9114816
• 负责人: Douglas Ulmer
• 金额: $ 3.89万
• 依托单位: University of Arizona
• 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: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9114816&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arthmetic; Elliptic; Curves

Professor Ulmer will work on the arithmetic of elliptic curves and automorphic forms over function fields. In particular, he intends to work on analogues of the conjecture of Mazur that asserts that the group of rational points on an elliptic curve defined over a function field over a finite field in a certain Zp extension is finitely generated. 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.

Ulmer教授将在功能领域的椭圆形曲线和自动形式的算术。 特别是，他打算对Mazur的猜想进行类似物的工作，该猜想断言，在某个ZP扩展中，在有限的ZP扩展中定义了椭圆曲线上定义的椭圆曲线上的合理点。 该项目属于算术几何形状的一般领域 - 一个融合了数学最古老的领域的主题：数字理论和几何形状。 事实证明，这种组合非常富有成果 - 最近解决了经受住几代人的问题。 其许多后果包括新的错误纠正代码。 此类代码对于现代计算机（硬盘）和紧凑磁盘都是必不可少的。