Mathematical Sciences: Shimura Varieties and Abelian Varieties

数学科学：志村簇和阿贝尔簇

• 批准号: 9203365
• 负责人: Alice Silverberg
• 金额: $ 6.76万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203365&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Shimura; Varieties; Abelian

Professor Silverberg will continue her work on Shimura varieties. In particular, she plans to study adelic representations attached to points on canonical models of arithmetic quotients of bounded symmetric domains. She also intends to work on questions about the fields obtained by adjoining torsion points on Abelian 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.

西尔弗伯格教授将继续她对志村的研究 品种 特别是，她计划研究阿德利克 表示附加到规范模型上的点 有界对称域的算术乘积 她还 打算研究有关领域的问题， Abel Varieties上的邻挠点 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。