Automorphic forms and arithmetic geometry

自守形式和算术几何

• 批准号: 1000228356-2012
• 负责人: Kudla, Stephen
• 金额: $ 3.64万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=695839
• 关键词: Automorphic; forms; arithmetic; geometry

Arithmetic geometry is concerned with the number theoretic properties of sets in n-dimensions defined by polynomial equations. The most important recent advances in this area -- Wiles' proof of Fermat's last theorem, for example -- have been achieved by establishing connections between integral points on such sets and automorphic forms, to which the techniques of analysis can be applied. The proposed research focuses on a new approach to establishing such connections based on the construction of generating series for arithmetic cycles, arithmetic theta series. This technique provides a method for calculating important number theoretic quantities, including arithmetic volumes, that were unattainable by earlier methods.

算术几何关注由多项式方程定义的 n 维集合的数论性质。该领域最重要的进步（例如，威尔斯的最后一个定理的证明）是通过在此类集合和自动形式上建立积分点之间的连接来实现的，可以应用分析技术。拟议的研究重点是基于算术循环的生成序列的构造，算术theta系列建立这种联系的新方法。该技术提供了一种计算重要数量理论量（包括算术容量）的方法，这些理论量是通过早期方法无法实现的。