Arithmetic and Geometry of Algebraic Varieties

代数簇的算术和几何

• 批准号: 0100277
• 负责人: Yuri Tschinkel
• 金额: $ 9.38万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-11-01 至 2004-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100277&HistoricalAwards=false
• 关键词: Arithmetic; Geometry; Algebraic; Varieties

The project addresses questions concerning the distribution ofrational and integral points on higher dimensional algebraic varieties.The main problem is to relate the Zariski density and the asymptoticdistribution of points to global geometric invariants.Number theory is one of the oldest branches of mathematics.Today it is marked by profound connections to geometryand analysis. It has a wide range of applications todata transmission, storage and cryptography. For example,many algorithms are based on arithmetic properties of elliptic curves.This research explores the higher dimensional case of surfacesand threefolds.

该项目解决了有关高维代数簇上有理点和积分点分布的问题。主要问题是将 Zariski 密度和点的渐近分布与全局几何不变量联系起来。数论是数学最古老的分支之一。今天它是与几何和分析有着深刻的联系。它在数据传输、存储和密码学方面有着广泛的应用。例如，许多算法都是基于椭圆曲线的算术特性。本研究探讨了曲面和三重的高维情况。