Mathematical Sciences: Arithmetic Algebraic Geometry

数学科学：算术代数几何

• 批准号: 9203843
• 负责人: Nicholas Katz
• 金额: $ 34.01万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203843&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Algebraic; Geometry

This grant supports the research of Professor N. Katz as principal investigator and Drs. H. Darmon and F. Rodriquez- Villegas as post-doctoral associates. Professor Katz will work on the l-adic cohomology of varieties over finite fields, the l-adic theory of exponential sums and the arithmetic theory of differential equations. Dr. Darmon will study relations between the arithmetic of schemes and the analytic properties of l-functions. Dr. Rodriquez-Villegas will study the arithmetic properties of special values of l-functions of CM-fields. 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.

这笔赠款支持N.Katz教授作为首席研究员，H.Darmon博士和F.Rodriquez-Villegas博士作为博士后助理的研究。Katz教授将致力于有限域上变元的L-adic上同调、指数和的L-adic理论和微分方程的算术理论的研究。Darmon博士将研究格式运算与L函数的解析性质之间的关系。Rodriquez-Villegas博士将研究CM-域的L函数的特殊值的算术性质。这个项目属于算术几何的一般领域--一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机(硬盘)和光盘都是必不可少的。