Mathematical Sciences: Mathematical Science: Modular forms, Elliptic curves and galois reprentations"

数学科学：数学科学：模形式、椭圆曲线和伽罗瓦表示"

• 批准号: 9224925
• 负责人: Andrew Wiles
• 金额: $ 27.01万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-05-01 至 1997-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9224925&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Science; Modular; forms

This award supports the research of Professor Wiles to work in number theory. The aim of this project is to try to prove that certain families of elliptic curves over the field of rationals is modular, the famous conjecture of Shimura-Taniyama-Weil. The approach will be to prove in general that suitable Galois representations with values in the two by two matrices , with entries in the field with three elements, always arise from modular forms. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.

该奖项支持怀尔斯教授的研究工作， 数论 这个项目的目的是试图证明， 有理数域上的某些椭圆曲线族是 模，著名的志村-谷山-韦伊猜想。 的 方法将是一般证明，适当的伽罗瓦 在2乘2矩阵中具有值的表示， 在三个元素的字段中的条目，总是由模块化产生 forms. 这是数论领域的研究。 数论 从整数和问题开始， 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。