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教授将致力于椭圆曲线和函数域自守形式的算术研究。 特别是，他打算研究 Mazur 猜想的类似问题，该猜想断言在某个 Zp 扩展中的有限域上的函数域上定义的椭圆曲线上的有理点组是有限生成的。 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。