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

这个项目是有关的几何，分层几何，丢芬图方面的相互关系，模和上同性的性质，和Shimura品种的积分正则模型的组合结构的前贝尔型和他们的特殊纤维。Shimura s晶体和Shimura Lie s晶体的新概念将用于攻击Langlands-Rapoport猜想，以及用于理解这些积分模型的特殊纤维的Lie正则分层。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Shimura预预型变体的zeta函数猜想。利用Arakelov交理论研究了Shimura型变分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，这个学科融合了数学中两个最古老的领域：数论和几何。事实证明，这种结合非常富有成效，最近解决了几代人经受住的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机和光盘都是必不可少的。

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.