Euler Systems and Their Applications

小行星9401321 该奖项资助了维克托·科利瓦金教授的研究。 Kolyvagin教授致力于欧拉系统理论及其在数论中的应用。 对于给定的欧拉系统，他计划扩展显式局部控制的上同调类集，并将它们与数域和椭圆曲线的算术联系起来。 这项研究福尔斯属于数论的总标题。数论是研究整数的性质，是数学最古老的分支。从一开始，数论中的问题就为这门学科的几乎所有部分的新数学的创造提供了动力。Kolyvagin教授是使用几何思想来研究整数的领导者。 这种数论非常技术性和深刻，但它在理论计算机科学和编码理论等领域有着惊人的应用。

9401321 Kolyvagin This award funds the research of Prof. Victor Kolyvagin. Prof. Kolyvagin works on the theory of Euler systems and their application to number theory. For a given Euler system, he plans to extend the set of cohomology classes explicitly controlled locally, and connect them to the arithmetic of number fields and elliptic curves. This research falls under the general heading of number theory. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished the driving force to creation of new mathematics in almost all parts of the discipline. Prof. Kolyvagin is a leader in the use of geometric ideas to study whole numbers. This kind of number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.