The Langlands Conjectures for Connected and Disconnected Groups

连通群和非连通群的朗兰兹猜想

• 批准号: 1801687
• 负责人: Tasho Kaletha
• 金额: $ 21.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1801687&HistoricalAwards=false
• 关键词: Langlands; Conjectures; Connected; Disconnected; Groups

This project investigates facets of the Langlands program -- an area of Mathematics bridging number theory and geometry that examines in a systematic way the symmetries inherent in solutions of algebraic equations. By relating these symmetries to geometry, the program creates a powerful way of obtaining arithmetic information. The project is particularly concerned with obtaining such information explicitly. Deep and explicit knowledge of the arithmetic of numbers is in turn essential for many technological advances over the last decades that we take for granted today, including encryption and digital security.In more detail, the project will establish a uniform and explicit construction of the refined local Langlands correspondence, for general connected reductive p-adic groups splitting over a tame extension and all supercuspidal parameters, in residual characteristic prime to the order of the Weyl group. The project further aims to compare the result of this construction with other more general but less explicit constructions, such as the one of Genestier-Lafforgue for local function fields. The role of disconnected groups will also be considered.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目调查方面的朗兰兹计划-数学领域的桥梁数论和几何学，以系统的方式检查固有的对称性的解决方案的代数方程。通过将这些对称性与几何学联系起来，该程序创建了一种获得算术信息的强大方法。该项目特别关注明确获取此类信息。在过去的几十年里，我们认为许多技术进步是理所当然的，包括加密和数字安全。更详细地说，该项目将建立一个统一的和明确的结构的精化局部朗兰兹对应，一般连接约化p-adic群分裂在一个驯服的扩张和所有超尖点参数，在剩余特征素数的顺序外尔群。该项目的进一步目标是将这种构造的结果与其他更一般但不太明确的构造进行比较，例如Genestier-Lafforgue的局部函数场构造。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

On the Kottwitz conjecture for local shtuka spaces

关于局部 shtuka 空间的 Kottwitz 猜想

• DOI: 10.1017/fmp.2022.7
• 发表时间: 2022
• 期刊: Forum of mathematics
• 作者: Hansen, David;Kaletha, Tasho;Weinstein, Jared
• 通讯作者: Weinstein, Jared

Regular Supercuspidal Representations

常规超尖角表示

• 发表时间: 2019
• 期刊: Journal of the American Mathematical Society
• 影响因子: 3.9
• 作者: Tasho Kaletha