Abelian Motives and Shimura Varieties

9622770米尔恩教授从事算术几何学的工作，专门研究丢番图几何中的问题。他将研究有限域上Shimura簇上的点上的Langland和Rapaport猜想。他还希望研究阿贝尔动机的退化，希望利用与下村品种的关系，以获得关于下村品种在数域上紧凑的信息。这个项目属于算术几何的一般领域--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(硬盘)和光盘都是必不可少的。?？

9622770 Milne Professor Milne works in arithmetic geometry specifically on problems in Diophantine geometry. He will study the conjecture of Langlands and Rapaport on points on Shimura varieties over finite fields. He also hopes to study the degeneration of abelian motives with the hope of exploiting the relation to Shimura varieties in order to obtain information about the compactifications of Shimura varieties over number fields. 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 (hard disks) and compact disks. ??