Mathematical Sciences: The Arithmetic of Shimura Varieties

该奖项支持詹姆斯·米尔恩教授的研究， 研究代数几何。 它已经被称为几个 几十年来，双方之间有着密切而富有成果的关系， 阿贝尔簇及其退化的算术， 一方面，Siegel模变量的算术， 另一方面是它们的紧化。 最近，教授 米尔恩发现了阿贝尔动机和 志村变种的阿贝尔型。 建议研究 阿贝尔型变性。 建议研究 阿贝尔动机的退化，并利用关系，以便 以获取志村致密化的信息 数域簇 这项研究使用代数几何的技术， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。如今，该领域 不仅使用代数方法，而且使用分析方法， 拓扑学，反过来说， 以及物理学、理论计算机科学， 机器人

This award supports the research of Professor James Milne to work in algebraic geometry. It has been known for several decades that there is a close and fruitful relation between the arithmetic of abelian varieties and their degenerations, on the one hand, and the arithmetic of Siegel modular varieties and their compactifications on the other hand. Recently, Professor Milne has found a similar relation between abelian motives and Shimura varieties of abelian type. It is proposed to study the degeneration of abelian type. It is proposed to study the degeneration of abelian motives and exploit the relation in order to obtain information about the compactifications of Shimura varieties over number fields This research uses the techniques of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.