Mathematical Sciences: Refined Conjectures of Birch and Swinnerton-Dyer Type, and Regular Algebras

数学科学：Birch 和 Swinnerton-Dyer 类型的精炼猜想以及正则代数

• 批准号: 9103772
• 负责人: John Tate
• 金额: $ 7.76万
• 依托单位: University of Texas at Austin
• 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: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103772&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Refined; Conjectures; Birch

Professor Tate will work on refined conjectures of Birch and Swinnerton-Dyer type. In particular, he will study a geometric analogue of this conjecture and its possible connections with two dimensional class field theory. He will also study regular graded associative algebras in dimensions greater than three. 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.

泰特教授将致力于桦树的精细结构， Swinnerton-Dyer型的 特别是，他将研究一个几何 这一猜想的类似物及其与两个可能的联系 维类场论 他还将学习定期分级 维数大于3的结合代数。 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。