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.

9970593 Kenneth Ribet打算继续他的工作与模形式，模曲线，阿贝尔品种和伽罗瓦群数论。 里贝特是特别感兴趣的领域所产生的扭转点的阿贝尔品种。 虽然这门学科中的许多问题本质上是技术性的，但它们最终都植根于寻找方程族的所有整数或分数解的经典问题。肯尼斯·里贝特研究模形式的算术，伽罗瓦表示和阿贝尔变种。 他的研究在于交叉代数几何和代数数论，两个蓬勃发展的数学领域。 里贝特最著名的贡献是他对费马大定理的证明：里贝特证明了一个关于伽罗瓦表示的技术性结果，有时被称为塞尔定理，它将费马大定理与椭圆曲线的志村-谷山猜想联系起来。 最近，里贝特对费马猜想的证明做出了贡献，该猜想认为三个不同的正完全n次幂（其中n大于2）永远不会形成一个算术级数。