Arithmetical Algebraic Geometry

算术代数几何

• 批准号: 9622801
• 负责人: Kenneth Ribet
• 金额: $ 18.89万
• 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: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622801&HistoricalAwards=false
• 关键词: Arithmetical; Algebraic; Geometry

This award provides funds for studies of modular forms, abelian varieties, and Galois representations. Gerhard Frey's construction, which associates triples of integers to elliptic curves over the rational numbers, has led to a direct link between the investigator's subject and simple problems involving whole numbers. Frey's construction has led to a proof of Fermat's Last Theorem and a resolution of several allied problems in mathematics. Many questions remain to be resolved - the ABC conjecture is perhaps the best known. One expects that arithmetic algebraic geometry will continue to flourish; the investigator is working on some of the problems that are now "on the table" as well as other problems which emerge over time. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

该奖项为模块化形式，阿贝尔品种和galois代表的研究提供了资金。格哈德·弗雷（Gerhard Frey）的构造将整数的三元组与椭圆形相关联，这导致了调查员的主题与涉及整数的简单问题之间的直接联系。弗雷（Frey）的构建导致了费玛特（Fermat）的最后定理证明，并解决了数学上几个盟友问题的解决方案。许多问题仍然有待解决 - ABC猜想也许是最著名的。人们期望算术代数几何形状将继续蓬勃发展。研究人员正在研究现在“桌子上”的一些问题，以及随着时间的流逝而出现的其他问题。 该项目属于算术几何形状的一般领域 - 一个融合了数学最古老的领域的主题：数字理论和几何学。 事实证明，这种组合非常富有成果 - 最近解决了经受住几代人的问题。 其许多后果包括新的错误纠正代码。 此类代码对于现代计算机（硬盘）和紧凑磁盘都是必不可少的。