Stark-Heegner points on elliptic curves over number fields

数域上椭圆曲线上的 Stark-Heegner 点

• 批准号: 355600-2008
• 负责人: Greenberg, Matthew
• 金额: $ 1.02万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=459472
• 关键词: Stark; Heegner; points; elliptic; curves

My research focuses on equations a special kind called elliptic curves. These equations arise in many branches of pure and applied mathematics. Due to their special structure, elliptic curves have recently found numerous important applications in the field of number theoretic cryptography. I am currently attempting to develop systematic methods for solving the equations defining elliptic curves. The key to these methods are a family of results (and conjectures) called modularity theorems, the prototype of which was proved in the 1990s by Andrew Wiles in his landmark proof of Fermat's Last Theorem.

我的研究集中在一种叫做椭圆曲线的特殊方程上。 这些方程出现在纯数学和应用数学的许多分支中。 椭圆曲线由于其特殊的结构在数论密码学中有着重要的应用。 我目前正试图开发系统的方法来解决定义椭圆曲线的方程。 这些方法的关键是一系列被称为模块性定理的结果（和结构），其原型在20世纪90年代由安德鲁·怀尔斯在他对费马大定理的里程碑式证明中证明。