Mathematical Sciences: Arithmetical Algebraic Geometry

数学科学：算术代数几何

• 批准号: 9306898
• 负责人: Kenneth Ribet
• 金额: $ 15.12万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306898&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetical; Algebraic; Geometry

This award supports the research of Professor Ribet to work in number theory. Since 1986, Ribet has been working on Serre's conjectures which relate mod p modular forms and mod p two dimensional representations of the Galois group of an algebraic closure of the rationals. Ribet also proposes to continue his interests in variants involving Shimura varieties, base fields other than the rationals and representation modulo powers of p. 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 Ribet 教授在数论方面的研究。 自 1986 年以来，Ribet 一直致力于 Serre 猜想，该猜想涉及有理数的代数闭包的 Galois 群的 mod p 模形式和 mod p 二维表示。 Ribet 还提议继续他对涉及 Shimura 变种的变体、除 p 的有理数和表示模幂之外的基础领域的兴趣。 这是数论领域的研究。 数论从整数和诸如一个整数能否被另一个整数整除之类的问题开始。 它是最古老的数学领域之一，最初纯粹出于美学原因而追求它。 然而，在过去的半个世纪中，它已成为开发计算机科学新算法和电子学新纠错码的重要工具。