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

Ribet 9705376这个项目关注的是几何之间的相互关系，分层几何，丢番图方面，模和上同调的性质，和组合结构的整正则模型的志村品种的preabel型和他们的特殊纤维。 志村s-晶体和志村李s-晶体的新概念将被用来攻击的Langlands-Rapoport猜想，以及了解这些积分模型的特殊纤维的李正则分层。 研究者将致力于更好地理解积分模型的几何，最终目标是证明志村变种的zeta函数猜想。 本文利用Arakelov交理论研究了前阿贝尔型Shimura簇积分模型中的丢番图问题。 这个项目福尔斯属于算术几何的一般领域，这是一个融合了两个最古老的数学领域：数论和几何的主题。 这种结合已被证明是非常富有成效的，最近解决了几代人的问题。 在它的许多后果是新的纠错码。 这种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.