Kazhdan-Laumon Representations and Langlands Correspondence

卡日丹-劳蒙交涉和朗兰兹通讯

• 批准号: 9800684
• 负责人: Alexander Beilinson
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9800684&HistoricalAwards=false
• 关键词: Kazhdan; Laumon; Representations; Langlands; Correspondence

9800684BeilinsonThis award supports a project by Alexander Braverman, a postdoctoral associate of A. Beilinson. This project consists of three parts. The first part is concerned with the study of general properties of the so-called Kazhdan-Laumon category, attached to a reductive group over a finite field, and some of its variants. Parts 2 and 3 are concerned with two possible applications of Kazhdan-Laumon category. The first one is connected with the geometric Langlands-Drinfeld conjecture. More precisely, we formulate a certain analog of the geometric Langlands conjecture for tamely ramified local systems on a projective curve over a finite field and propose to prove it in some cases. This formulation involves the definition of the Kazhdan-Laumon category. We also propose to study the so called geometric Eisenstein series sheaves. The last part of the project concerns with a possible application to representation theory of finite Chevalley groups and character sheaves, extending the work started in Braverman's Ph. D. thesis.This proposal is in the part of mathematics known as the Langlands program. The Langlands program is part of number theory. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langlands program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. One aspect of this proposal is to explore the applications of geometric techniques within the Langlands program.

该奖项支持A.Beilinson的博士后助理Alexander Braverman的一个项目。这个项目由三个部分组成。第一部分研究了有限域上的约化群上的所谓Kazhdan-Laumon范畴及其变种的一般性质。第二部分和第三部分是关于Kazhdan-Laumon范畴的两个可能的应用。第一个与几何的朗兰兹-德因费尔德猜想有关。更确切地说，对于有限域上射影曲线上的温和分枝局部系统，我们建立了几何朗兰兹猜想的某种类似形式，并在某些情况下给出了证明。这一提法涉及Kazhdan-Laumon范畴的定义。我们还建议研究所谓的几何Eisenstein系列滑轮。项目的最后部分涉及到有限Chvalley群和特征标的表示理论的可能应用，扩展了Braverman博士论文中开始的工作。这项建议是在被称为朗兰兹计划的数学部分。朗兰兹计划是数论的一部分。数论是研究全体数的性质的学科，是数学中最古老的分支。从一开始，数论中的问题就为在该学科的其他不同部分创造新的数学提供了动力。朗兰兹计划是一种将数论与微积分联系起来的一般哲学；它体现了研究整数的现代方法。这项提议的一个方面是探索几何技术在朗兰兹计划中的应用。