Arithmetic geometry and algebraic number theory

算术几何与代数数论

• 批准号: 1000231449-2017
• 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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=694209
• 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.

解决数学方程是人类寻求知识的重要方面。在此框架内，可以探索以有理数为系数的求解方程。 为此，需要了解理性数字领域的可能的领域扩展，这些解决方案可能在其中。在数学列表中，人们需要了解理性数字领域的Galois组的结构。拉姆多莱（Ramdorai）试图使用来自动机理论的伊瓦沙（Iwasawa）理论中的工具来探索加洛伊斯集团（Galois group）。代数数理论的进步最近几个世纪通常是研究此中心问题的直接结果。