Mathematical Sciences: Algebra & Number Theory: Shimura Varieties

数学科学：代数

• 批准号: 9001357
• 负责人: Alice Silverberg
• 金额: $ 4.26万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1992-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001357&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebra; & Number

This award supports the research in arithmetic algebraic geometry of Professor Alice Silverberg of The Ohio State University. Dr. Silverberg's project is to study arithmetic quotients of bounded symmetric domains and their points, and especially certain special group representations associated to such points. 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.

该奖项支持俄亥俄州立大学 Alice Silverberg 教授的算术代数几何研究。 Silverberg 博士的项目是研究有界对称域及其点的算术商，特别是与这些点相关的某些特殊群表示。 这是算术代数几何领域的研究，是一门结合了代数几何和数论技术的学科。在其最初的表述中，代数几何处理可以通过最简单的方程（即多项式）在平面中定义的图形。数论始于整数以及诸如一个整数能否被另一个整数整除之类的问题。这两个看似相距甚远的学科，实际上从很早开始就相互影响，而且在过去的四分之一个世纪里，相互影响力大大增强。算术代数几何领域现在使用所有现代数学的技术，并在其自身边界之外产生相应的影响。