Euler Systems and Their Applications

欧拉系统及其应用

• 批准号: 9401321
• 负责人: Victor Kolyvagin
• 金额: $ 7.64万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401321&HistoricalAwards=false
• 关键词: Euler; Systems; Their; Applications

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.

9401321 Kolyvagin 该奖项资助 Victor Kolyvagin 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，他计划扩展局部显式控制的上同调类集，并将它们连接到数域和椭圆曲线的算术。 这项研究属于数论的总标题。数论是对整数性质的研究，是数学最古老的分支。从一开始，数论中的问题就为该学科几乎所有部分的新数学创造提供了动力。 Kolyvagin 教授是利用几何思想研究整数方面的领导者。 这种数论非常技术性和深奥，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。