The Arithmetic of Integral Canonical Models of Shimura Varieties of Preabelian Type

普雷贝拉型志村品种的积分正则模型的算法

• 批准号: 9705376
• 负责人: Kenneth Ribet
• 金额: $ 4.79万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9705376&HistoricalAwards=false
• 关键词: Arithmetic; Integral; Canonical; Models; Shimura

Ribet 9705376 This project is concerned with the interrelation between the geometry, the stratified geometry, the diophantine aspects, the modular and cohomology properties, and the combinatorial structure of the integral canonical models of Shimura varieties of preabelian type and of their special fibres. New notions of Shimura s-crystals and Shimura Lie s-crystals will be used to attack the Langlands-Rapoport conjecture, as well as for understanding the Lie canonical stratification of the special fibres of these integral models. The investigator will work on a better understanding of the geometry of integral models with the ultimate goal being a proof of the zeta function conjecture for Shimura varieties of preabelian type. The Arakelov intersection theory will be used to study the Diophantine problems in integral models of Shimura varieties of preabelian type. 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 and compact disks.

Ribet 9705376 该项目涉及几何学、分层几何学、丢番图方面、模和上同调性质以及前阿贝尔型 Shimura 品种及其特殊纤维的积分正则模型的组合结构之间的相互关系。 Shimura s 晶体和 Shimura Lie s 晶体的新概念将用于攻击 Langlands-Rapoport 猜想，以及理解这些积分模型的特殊纤维的 Lie 规范分层。 研究人员将致力于更好地理解积分模型的几何形状，最终目标是证明前阿贝尔型 Shimura 变体的 zeta 函数猜想。 Arakelov 交集理论将用于研究前阿贝尔型 Shimura 变体积分模型中的丢番图问题。 该项目属于算术几何的一般领域，该学科融合了两个最古老的数学领域：数论和几何。 事实证明，这种结合非常富有成效，最近解决了几代人面临的问题。 其众多后果之一就是新的纠错码。 此类代码对于现代计算机和光盘都是必不可少的。