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该项目与几何形状，分层几何形状，区分剂方面，模块化和共同体学特性以及比贝氏类型Shimura品种的积分规范模型的组合结构之间的相互关系。 Shimura S-晶体和Shimura Lie S-Crystal的新概念将用于攻击Langlands-Ropoport的猜想，以及了解这些积分模型的特殊纤维的谎言规范分层。 研究人员将更好地理解积分模型的几何形状，最终目标是证明Zeta功能的shimura shimura typer of preabelian类型。 Arakelov交叉路口理论将用于研究preabelian类型的Shimura品种的整体模型中的双磷酸问题。 该项目属于算术几何形状的一般领域，该主题融合了数学的两个最古老的领域：数字理论和几何形状。 事实证明，这种组合非常富有成果，而最近解决了经受住几代人的问题。 其许多后果包括新的错误纠正代码。 此类代码对于现代计算机和紧凑型磁盘都是必不可少的。