L-Functions of Algebraic Varieties Over Finite Fields

有限域上代数簇的 L 函数

• 批准号: 9970417
• 负责人: Daqing Wan
• 金额: $ 20.8万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970417&HistoricalAwards=false
• 关键词: Functions; Algebraic; Varieties; Over; Finite

Abstract Daquing Wan UC Irvine 9970417 Professor Wan will continue his study of the p-adic of L-functions arising from algebraic geometry over a finite field of characteristic p. The central problem in this study is a 1973 conjecture of Dwork about the p-adic continuation of the L function of a unit root F-chrystal. Prof. Wan will try to establish the general validity of this conjecture. He will also investigate the arithmetic consequences of the conjecture including higher dimensional generalizations of the Gouvea-Mazur conjecture, and the zeros of certain geometric L-functions, and the connections with the mysterious mirror map that arises from a family of Calabi-Yau varieties. This is a project in number theory and algebraic geometry. One of mathematics oldest branches, number theory is the study of numbers that can be expressed exactly in terms of the simplest counting numbers, 1, 2, 3, 4, 5. In the second half of this century, modern geometry has had a tremendous impact on number theory introducing new methods and new problems. The development of algebraic geometry has paralleled advances in number theory for the past 30 years. Professor Wan will study geometric objects defined over the simplest possible mathematical basis for such a geometry, a finite field. These are simultaneously the simplest and most intriguing objects in algebraic geometry. They have found very practical application in communications, security, and other surprising areas.

万大青教授将继续研究特征为p的有限域上的代数几何中L-函数的p-adic问题。本研究的中心问题是Dwork于1973年提出的关于单位根F-晶体的L-函数的p-adic延拓的一个猜想。万教授将试图证明这一猜想的普遍有效性。 他还将研究该猜想的算术后果，包括Gouvea-Mazur猜想的高维推广，某些几何L函数的零点，以及与来自Calabi-Yau变种家族的神秘镜像映射的联系。这是一个数论和代数几何的项目。 数学最古老的分支之一，数论是研究可以用最简单的计数数字1，2，3，4，5来精确表达的数字。 在本世纪的后半叶，现代几何学对数论产生了巨大的影响，引入了新的方法和新的问题。 在过去的30年里，代数几何的发展促进了数论的发展。万教授将研究几何对象定义在最简单的数学基础，这样的几何，有限的领域。 这些同时是最简单和最有趣的对象在代数几何。它们在通信、安全和其他令人惊讶的领域中得到了非常实际的应用。