Singular moduli on Shimura curves

Shimura 曲线上的奇异模量

• 批准号: 312426-2006
• 负责人: Baba, Srinath
• 金额: $ 0.36万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=363493
• 关键词: Singular; moduli; Shimura; curves

My work is on studying Shimura curves, which are parameter spaces of certain surfaces called QM abelian surfaces. The theory of Shimura curves is expected to resemble the theory of Modular curves as the two are very connected. The theory of Modular curves has been very instrumental in the solution of Fermat's Last Theorem, and many other important mathematical problems. My work is based on extending known results from Modular curves to Shimura curves, my results are very computational and thus have wide application.

我的工作是研究志村曲线，这是参数空间的某些曲面称为QM交换曲面。志村曲线的理论预计类似于模曲线的理论，因为两者非常相关。模曲线理论在解决费马大定理和许多其他重要的数学问题中起到了非常重要的作用。我的工作是基于推广已知的结果从模曲线到志村曲线，我的结果是非常计算，因此有广泛的应用。