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: $ 14.57万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=656075
• 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.

算术几何关注的是由多项式方程定义的n维集合的数论性质。最近在这一领域最重要的进展--例如怀尔斯对费马最后定理的证明--是通过建立这样的集合上的整点与自守形式之间的联系而实现的，分析技术可以应用于这种联系。建议的研究重点是一种新的方法来建立这样的连接的基础上建设的生成系列的算术周期，算术θ系列。这种技术提供了一种计算重要的数论量的方法，包括算术体积，这是以前的方法无法实现的。