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.

乌尔默教授将致力于椭圆的算术 函数域上的曲线和自守形式。 在 特别是，他打算工作的类似物的猜想， Mazur断言，一个集合上的有理点群 有限域上函数域上的椭圆曲线 在某个Zp扩展中，它是随机生成的。 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 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。