Serre-type conjectures and mod p Langlands correspondences

Serre 型猜想和 mod p Langlands 对应

• 批准号: 402885-2012
• 负责人: Herzig, Florian
• 金额: $ 2.19万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=529688
• 关键词: Serre; type; conjectures; mod; Langlands

Number theory is the study of whole numbers and the solvability of equations in whole numbers. It is one of the oldest branches of mathematics. One particularly famous problem is Fermat's Last Theorem, which concerns the insolvability in the integers of certain simple equations. It was only solved some 15 years ago, by establishing a deep connection between elliptic curves (objects of geometry) and modular forms (objects of analysis and the theory of symmetries). This deep connection is a special instance of the Langlands Program, which consists of a number of very general and interlinked conjectures that, in particular, help to explain many phenomena in number theory.

数论是研究整数和整数方程的可解性的学科。它是数学最古老的分支之一。一个特别著名的问题是费马大定理，它涉及某些简单方程的整数不可解性。直到15年前，通过在椭圆曲线（几何对象）和模形式（分析对象和对称性理论）之间建立深刻的联系，这个问题才得到解决。这种深层联系是朗兰兹纲领的一个特殊例子，朗兰兹纲领由许多非常普遍和相互关联的理论组成，特别有助于解释数论中的许多现象。