Arithmetic Algebraic Geometry

算术代数几何

• 批准号: 0106588
• 负责人: Nicholas Katz
• 金额: $ 29.6万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-15 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0106588&HistoricalAwards=false
• 关键词: Arithmetic; Algebraic; Geometry

This is a project in the area of mathematics called number theory. Professor Katz will investigate varieties defined over finite fields, in particular their cohomology and the distribution of the zeros of L functions on such varieties.This is a project in the area of mathematics called number theory. The main focus of this project can be described as the study of certain kinds of solutions to polynomial equations called "modular solutions." Many of the applications computer scientists have for number theory involve these kinds of solutions. Professor Katz is considering questions involving the number of such solutions, how this number changes as the polynomials change, and how the solution sets of different polynomials are related.

这是一个数学领域的项目，叫做数论。 Katz教授将研究在有限域上定义的簇，特别是它们的上同调和L函数在这些簇上的零点分布。这是数学领域的一个项目，称为数论。 这个项目的主要重点可以描述为研究多项式方程的某些类型的解决方案，称为“模块解决方案”。“计算机科学家对数论的许多应用都涉及这类解决方案。 卡茨教授正在考虑的问题涉及到这样的解决方案的数量，这个数字如何随着多项式的变化而变化，以及不同多项式的解决方案集如何相关。