Mathematical Sciences: Sheaves on Witt Schemes and Trace Formula with Application to Representation Theory

数学科学：维特方案和迹公式及其在表示论中的应用

• 批准号: 9700458
• 负责人: Alexander Polishchuk
• 金额: $ 8.25万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700458&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Sheaves; Witt; Schemes

Polishchuk 9700458 This research is concerned with generalizing the approach of character sheaves from the case of groups over finite fields to groups over p-adic fields. The work involves two parts. The first part is to devise a notion of sheaves on ind-schemes mimicking that of locally-constant functions on p-adic varieties. The second part is to generalize the Lefschetz-Verdier trace formula and its application to the construction of the discrete series representation of a reductive group over a finite field based on the gluing of perverse sheaves. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.

这项研究与PolishChuk 9700458有关，涉及将群体的角色滑轮的方法概括为有限领域的p-Adic领域的组。 这项工作涉及两个部分。 第一部分是在模仿P-Adic品种上的局部构成功能的Indshemes上设计一个束带的概念。 第二部分是概括lefschetz-verdier痕量公式，并将其应用于基于有限滑轮的粘合而在有限场上的离散串联表示的构建。 这是代数几何学领域的研究。 代数几何形状是现代数学最古老的部分之一，但在过去的25年中，它具有革命性的开花。 它起源于它处理的数字可以通过最简单的方程（即多项式）在平面中定义的数字。 如今，该领域不仅利用了来自代数的方法，还利用了分析和拓扑的方法，相反，在这些领域以及物理，理论计算机科学和机器人技术中找到了应用。