Mathematical Sciences: Arithmetic Geometry

数学科学：算术几何

• 批准号: 9204805
• 负责人: Ching-Li Chai
• 金额: --
• 依托单位: University of Pennsylvania
• 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 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204805&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Geometry

Professor Chai on several problems in arithmetic geometry. These include canonical integral models of Shimura varieties and the theory of p-adic symmetric spaces with a view to an analogue of Schmidt's theorem on degenerations of Hodge structures. 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.

柴教授谈算术几何中的几个问题。 这些包括典型的积分模型志村品种和 p-adic对称空间理论及其类比 关于Hodge结构退化的施密特定理。 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。