Mathematical Sciences: Level Structures on Abelian Varieties

数学科学：阿贝尔簇的能级结构

• 批准号: 9000567
• 负责人: Peter Norman
• 金额: $ 4.92万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000567&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Level; Structures; Abelian

This award supports the research on level structures for Abelian varieties of Professor Peter Norman of the University of Massachusetts. Dr. Norman's work will involve the problems of lifting Abelian varieties from positive characteristic to zero characteristic, as well as researches on Hilbert-Blumenthal varieties and Dieudonne theory. This is research in the field of arithmetic algebraic geometry, a subject that combines the techniques of algebraic geometry and number theory. In its original formulation, algebraic geometry treated figures that could be defined in the plane by the simplest equations, namely polynomials. Number theory started with the whole numbers and such questions as divisibility of one whole number by another. These two subjects, seemingly so far apart, have in fact influenced each other from the earliest times, but in the past quarter century the mutual influence has increased greatly. The field of arithmetic algebraic geometry now uses techniques from all of modern mathematics, and is having corresponding influence beyond its own borders.

该奖项支持对层次结构的研究， 阿贝尔变种的彼得诺曼教授的大学 马萨诸塞州。诺曼博士的工作将涉及以下问题 将阿贝尔簇从正特征提升到零 特点，以及对希尔伯特-布卢门撒尔的研究 变种和迪厄多内理论。 这是算术代数领域的研究 几何学是一门结合了代数和几何学技巧的学科。 几何学和数论在其最初的提法中， 代数几何处理的图形，可以定义在 平面由最简单的方程，即多项式。Number 理论开始于整数， 一个整数被另一个整数整除。这两个主题， 看似相隔甚远，实际上却相互影响， 但在过去的四分之一世纪， 影响力大增。算术领域 代数几何现在使用的技术， 数学，并具有相应的影响力超出其本身 边境