Arithmetical Algebraic Geometry

算术代数几何

• 批准号: 9970593
• 负责人: Kenneth Ribet
• 金额: $ 13.5万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970593&HistoricalAwards=false
• 关键词: Arithmetical; Algebraic; Geometry

9970593Kenneth Ribet intends to continue his work on the number theory associated with modular forms, modular curves, abelian varieties and Galois groups. Ribet is especially interested in number fields arising from torsion points on abelian varieties. While many questions in this subject are technical in nature, they are ultimately rooted in the classical problem of finding all whole number or fractional solutions to a family of equations.Kenneth Ribet studies the arithmetic of modular forms, Galois representations and abelian varieties. His research lies at the intersection of algebraic geometry and algebraic number theory, two flourishing fields of mathematics. Ribet is best known for his contribution to the proof of Fermat's Last Theorem: Ribet proved a technical result about Galois representations, sometimes known as Serre's epsilon conjecure, which relates Fermat's Last Theorem to the Shimura-Taniyama conjecture for elliptic curves. More recently, Ribet contributed to the proof of a Fermat's conjecture to the effect that three distinct positive perfect n'th powers (where n is bigger than 2) can never form an arithmetic progression.

9970593Kenneth Ribet打算继续对与模块化形式，模块化曲线，Abelian品种和Galois组相关的数字理论进行工作。 Ribet对阿贝里亚品种上的扭转点产生的数字尤其感兴趣。 尽管该主题的许多问题本质上是技术性的，但最终它们源于为方程式家庭找到所有整数或分数解决方案的经典问题。 他的研究在于代数几何学和代数数理论的交集，这是两个蓬勃发展的数学领域。 Ribet以他对Fermat的最后一个定理证明的贡献而闻名：Ribet证明了有关Galois表示的技术结果，有时被称为Serre的Epsilon Conjecure，这将Fermat的最后一个定理与Shimura-Taniyama的最后一个定理有关椭圆曲线的猜想。 最近，Ribet有助于证明Fermat的猜想，即三个独特的正面完美N'th能力（其中N大于2）永远不会形成算术进展。