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教授的研究工作， 数论 自1986年以来，里贝特一直致力于塞尔的 模p模形式与模p二的关系 代数的伽罗瓦群的维数表示 理性的终结。 里贝特还建议继续他的 利益的变种涉及志村品种，基地领域 除了p的有理数和表示模幂之外。 这是数论领域的研究。 Number 理论开始于整数和问题，如 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。