Mathematical Sciences: Arithmetic Geometry

数学科学：算术几何

• 批准号: 9002574
• 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: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002574&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Geometry

This award supports the research in arithmetic algebraic geometry of Professor Ching-Li Chai of the University of Pennsylvania. Dr. Chai has proposed to work on two projects: the first is to investigate level structures over extraordinary primes, and the second is to construct rigid homogeneous spaces. Both of these projects are related to the arithmetic of automorphic forms and Shimura varieties. This is research in the field of arithmetic algebraic geometry, a subject that combines the techniques of algebraic geometry and number theory. In its original formulation, algebraic geometry treated figures that could be defined in the plane by the simplest equations, namely polynomials. Number theory started with the whole numbers and such questions as divisibility of one whole number by another. These two subjects, seemingly so far apart, have in fact influenced each other from the earliest times, but in the past quarter century the mutual influence has increased greatly. The field of arithmetic algebraic geometry now uses techniques from all of modern mathematics, and is having corresponding influence beyond its own borders.

该奖项支持算术代数的研究 香港中文大学教授柴庆立教授的几何学 宾夕法尼亚柴博士建议从事两个项目： 第一是研究非平凡的层次结构， 素数，第二个是构造刚性齐性空间。 这两个项目都涉及到 自守型和志村变种。 这是算术代数领域的研究 几何学是一门结合了代数和几何学技巧的学科。 几何学和数论在其最初的提法中， 代数几何处理的图形，可以定义在 平面由最简单的方程，即多项式。Number 理论开始于整数， 一个整数被另一个整数整除。这两个主题， 看似相隔甚远，实际上却相互影响， 但在过去的四分之一世纪， 影响力大增。算术领域 代数几何现在使用的技术， 数学，并具有相应的影响力超出其本身 边境