Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

数学科学：算术几何和 K 理论主题

• 批准号: 9203379
• 负责人: Henri Gillet
• 金额: $ 8.29万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-05-01 至 1995-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203379&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Arithmetic; Geometry

Professor Gillet will continue his work on Arakelov theory and arithmetic Riemann-Roch type theorems. He will also work on Gersten's conjecture in Algebraic K-theory and connections between Lichtenbaum's conjectures on K-theory and Regulators and arithmetic intersection theory. 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.

吉莱教授将继续他对阿拉克洛夫理论的研究 和算术Riemann-Roch型定理。 他还将致力于 代数K-理论中的Gersten猜想与联系 Lichtenbaum关于K理论和调节器的论述之间， 算术交理论 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。