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这个项目涉及前阿贝尔型Shimura变种及其特殊纤维的整体正则模型的几何、分层几何、丢番图方面、模和上同调性质以及组合结构之间的相互关系。下村S晶体和下村李S晶体的新概念将被用来攻击朗兰兹-拉波波特猜想，并用来理解这些积分模型中特殊纤维的李正则分层。研究人员将致力于更好地理解积分模型的几何，最终目标是证明前阿贝尔型Shimura变种的Zeta函数猜想。利用Arakelov交理论研究前阿贝尔型Shimura簇积分模型中的丢番图问题。这个项目属于算术几何的一般领域，这是一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效，最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机和光盘来说都是必不可少的。