Mathematical Sciences: Arithmetic of Motives and Shimura Varieties

数学科学：动机算术和志村簇

• 批准号: 9304289
• 负责人: Don Blasius
• 金额: $ 7.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304289&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Motives; Shimura

Professor Blasius will continue his work on Shimura varieties and their associated motives. He will study motives attached to Hilbert modular forms using the stable trace formula and endoscopy. He will also study reductions mod p of these varieties. 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.

Blasius教授将继续他关于志村变种及其相关动机的研究。他将使用稳定的轨迹公式和内窥镜来研究希尔伯特模形式的动机。他还将研究这些品种的减少模式。这个项目属于算术几何的一般领域，这门学科融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。