Mathematical Sciences: Intersection Theory and P-adic Dynamical Systems

数学科学：交集理论和 P-adic 动力系统

• 批准号: 9500982
• 负责人: Kevin Keating
• 金额: --
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500982&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Intersection; Theory; adic

Keating 9500982 Professor Keating will work on problems in arithmetic geometry. He will try to compute the arithmetical intersection numbers for certain divisors on moduli spaces of abelian varieties. He also will study the general theory of p-adic dynamical systems from he point of view of the field of norms. Finally he wishes to study the actions of certain automorphism groups of formal groups on the moduli space of deformations of that group. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

基廷教授将研究算术几何方面的问题。他将尝试计算阿贝尔变体的模空间上某些除数的算术交数。他还将从范数领域的角度研究p进动力系统的一般理论。最后，研究了形式群的某些自同构群在该群变形模空间上的作用。这个项目属于算术几何的一般领域，它融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。