Abelian Motives and Shimura Varieties

小行星9622770 米尔恩教授的作品在算术几何特别是在丢番图几何问题。他将研究猜想朗兰兹和拉帕波特点志村品种有限领域。他还希望研究阿贝尔动机的退化，希望利用与志村品种的关系，以获得有关数域上志村品种紧化的信息。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 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. ??