Galois structure, Iwasawa theory and arithmetic geometry

伽罗瓦结构、岩泽理论和算术几何

• 批准号: 0401319
• 负责人: Adebisi Agboola
• 金额: $ 10.5万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0401319&HistoricalAwards=false
• 关键词: Galois; structure; Iwasawa; theory; arithmetic

The Principal Investigator will conduct research in two areas that willlead to new results in number theory and arithmetic geometry. Thefirst is concerned with several questions that are centerd aroundconjectures of Birch and Swinnerton-Dyer type. These questions involvearithmetic Galois module structure, Iwasawa theory and Arakelovtheory. The second topic deals with the study of relative Galoisstructure invariants using techniques from relative algebraicK-theory.The research described in this proposal lies in the field ofarithmetic algebraic geometry. This is a subject that blends two ofthe oldest branches of mathematics, namely number theory andgeometry. It has now blossomed to a point where it has resolvedproblems that have stood for centuries--the most famous recent exampleof this is the resolution of Fermat's Last Theorem by Andrew Wiles. Inaddition to its central importance within mathematics, this area hasfar-reaching concrete applications in fields as diverse as physics,robotics, data processing and information theory.

首席研究员将在两个领域进行研究，这将导致数论和算术几何的新成果。第一个是关于围绕Birch和Swinnerton-Dyer型结构的几个问题。这些问题涉及算术Galois模结构、Iwasawa理论和Arakelov理论。第二个主题是用相对代数K-理论的方法研究相对伽罗瓦结构不变量，本论文所述的研究属于算术代数几何领域。这是一门融合了两个最古老的数学分支，即数论和几何学的学科。它现在已经发展到解决了几个世纪以来的问题--最近最著名的例子是安德鲁·怀尔斯对费马大定理的解决。除了它在数学中的核心重要性，这一领域在物理学，机器人技术，数据处理和信息理论等领域有着深远的具体应用。