Mathematical Sciences: Integral Hecke Structures, Crystalline Cohomology, & GL(2) Over Totally Real Fields

数学科学：积分赫克结构、晶体上同调、

• 批准号: 9402866
• 负责人: Bruce Jordan
• 金额: $ 5.32万
• 依托单位: CUNY Baruch College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9402866&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integral; Hecke; Structures

Jordan This award funds the research of Professor Bruce Jordan into the Hecke structure of Shimura varieties. Recent advances in crystalline cohomology make it possible to control the action of inertia on p-adic cohomology groups of varieties over unramified extensions with good reduction over the rational p-adic field. Prof. Jordan expects to apply these techniques to Shimura varieties. 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 result has been an increased understanding of both areas of mathematics. ***

约旦 该奖项资助了布鲁斯乔丹教授对志村品种的赫克结构的研究。 结晶上同调的最新进展使得在有理p-adic域上控制惯性对非分歧扩张簇的p-adic上同调群的作用成为可能。 乔丹教授希望将这些技术应用于志村品种。 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。这两个看似相距甚远的主题，实际上相互影响， 但在过去的四分之一世纪， 影响力大增。其结果是增加了对这两个数学领域的理解。***