Iwasawa Theory and Arithmetic Geometry

岩泽理论与算术几何

• 批准号: 9700937
• 负责人: Adebisi Agboola
• 金额: $ 7.5万
• 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: 1997
• 资助国家: 美国
• 起止时间: 1997-07-15 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700937&HistoricalAwards=false
• 关键词: Iwasawa; Theory; Arithmetic; Geometry

Agboola 9700937 This award will fund research on two topics in arithmetic algebraic geometry. The first is concerned with Iwasawa theory and L-functions. The PI will study new approaches to the Birch and Swinnerton-Dyer conjecture and the theory of p-adic L-functions. These approaches have their origins in the theory of arithmetic Galois module structure, and they lead to new ways of studying the Iwasawa theory of abelian varieties and p-adic representations. The second topic deals with equivariant algebraic geometry and the K-theory of higher dimensional varieties over finite fields. The PI will study reduced Grothendieck groups of equivariant vector bundles on varieties. He will develop the geometry of locally free class groups in positive characteristic, and he will explore connections with higher-dimensional class field theory and crystalline cohomology. The research described in this proposal lies in the field of arithmetic algebraic geometry. This is a subject that blends two of the oldest branches of mathematics---number theory and geometry---and which has blossomed to the point where it has solved problems that have stood for centuries. It finds applications in fields as diverse as physics, robotics, data processing and information theory.

Agboola 9700937 该奖项将资助算术代数几何两个主题的研究。第一个是关于岩泽理论和L-函数。PI将研究Birch和Swinnerton-Dyer猜想以及p-adic L-函数理论的新方法。这些方法起源于算术伽罗瓦模结构理论，它们为研究阿贝尔簇和p-adic表示的岩泽理论提供了新的方法。第二个主题涉及等变代数几何和有限域上高维簇的K-理论。PI将研究品种上的等变向量丛的约化Grothendieck群。他将开发的几何局部自由类群体的积极特点，他将探讨连接与高维类领域理论和结晶上同调。 本建议中所述的研究属于算术代数几何领域。这门学科融合了数学中两个最古老的分支-数论和几何-并且已经发展到解决了几个世纪以来一直存在的问题的地步。它在物理学、机器人学、数据处理和信息论等不同领域都有应用。