Mathematical Sciences: Shimura Varieties and Endoscopy

数学科学：志村品种和内窥镜检查

• 批准号: 9203380
• 负责人: Robert Kottwitz
• 金额: $ 17.83万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203380&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Shimura; Varieties; Endoscopy

Professor Kottwitz will work on several problems connected with automorphic forms. In particular, he will study endoscopy and its applications to Shimura varieties. He will also work on the stable version of Arthur's trace formula, problems of bad reduction of Shimura varieties and connections between the stable trace formula and the Lefschetz fixed point formula. Automorphic forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.

Kottwitz 教授将研究与自同构相关的几个问题。 他将特别研究内窥镜检查及其在志村品种中的应用。 他还将研究 Arthur 迹公式的稳定版本、Shimura 簇的不良约简问题以及稳定迹公式与 Lefschetz 不动点公式之间的联系。 自守形式起源于十九世纪中叶的非欧几里得几何。 数学家和物理学家很早就认识到，许多具有根本重要性的物体的基本性质都是非欧几里得的。 该领域主要关注有关整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系，从而与理论物理学中的规范理论和信息论中的编码理论等不同领域的问题保持联系。