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教授在数字理论中起作用的研究。 自1986年以来，Ribet一直在研究Serre的猜想，该猜想将Mod P模块化形式和Mod P p二维表示，该代数封闭的理性闭合。 Ribet还建议继续他对涉及Shimura品种的变体的兴趣，除了p的理性和代表性以外的基本场外。 这是数字理论领域的研究。 数字理论始于整个数字和问题，例如一个整数的划分。 它是数学最古老的领域之一，最初是出于纯粹的审美原因而追求的。 但是，在过去的半个世纪中，它已成为开发用于计算机科学的新算法的重要工具，并为电子设备纠正新的错误代码。