Arithmetic Geometry And Algebraic Number Theory

算术几何与代数数论

• 批准号: CRC-2017-00306
• 负责人: Ramdorai, Sujatha
• 金额: $ 14.57万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=730215
• 关键词: Arithmetic; Geometry; Algebraic; Number; Theory

Solving mathematical equations is an important aspect of humanity's quest for knowledge. Within this framework, one can explore solving equations which have rational numbers as coefficients. For this, one needs to understand possible field extensions of the field of rational numbers, where such solutions might lie. In mathematical parlance, one needs to understand the structure of the Galois group of the field of rational numbers. Ramdorai seeks to explore the Galois group using tools from Iwasawa theory, the theory of motives. Advances in Algebraic Number Theory in recent centuries are often a direct result of studying this central problem.

解数学方程式是人类求知的一个重要方面。在这个框架内，人们可以探索以有理数为系数的方程的求解。为此，人们需要了解有理数域的可能的域扩展，这样的解决方案可能存在于那里。在数学术语中，人们需要了解有理数领域的伽罗瓦群的结构。Ramdorai试图使用岩泽理论、动机理论中的工具来探索伽罗瓦集团。近几个世纪来代数数论的进步往往是研究这一中心问题的直接结果。