Mathematical Sciences: Diophantine Approximations of Algebraic Points

数学科学：代数点的丢番图近似

• 批准号: 9001372
• 负责人: Paul Vojta
• 金额: $ 6.77万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001372&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Diophantine; Approximations; Algebraic

This award supports the research in Diophantine approximations of Professor Paul Vojta of the University of California at Berkeley. Dr. Vojta's project is to extend his already-productive analogy between Nevanlinna Theory and Diophantine approximation theory, so as to get information on algebraic points of bounded degree on varieties. In addition, he hopes to generalize to varieties of higher dimension his independent proof of the Mordell-Faltings Theorem that arose from applying his viewpoint to Dyson's sharpening of the Thue-Siegel Theorem. 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.

该奖项支持丢番图的研究 大学教授Paul Vojta的近似值 加州伯克利分校。沃伊塔博士的项目是 内万林纳理论和 丢番图近似理论，以便获得有关 簇上有界度的代数点。此外他 他希望将其推广到更高维的各种类型， Mordell-Faltings定理的独立证明， 将他的观点应用于戴森对Thue-Siegel的锐化， 定理 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