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. ***

乔丹 该奖项资助布鲁斯·乔丹教授对志村品种赫克结构的研究。 晶体上同调的最新进展使得控制簇的 p-adic 上同调群上的惯性作用成为可能，在无分支延拓上，并在有理 p-adic 场上得到良好的简化。 乔丹教授希望将这些技术应用于志村品种。 这是算术代数几何领域的研究，是一门结合了代数几何和数论技术的学科。在其最初的表述中，代数几何处理可以通过最简单的方程（即多项式）在平面中定义的图形。数论始于整数以及诸如一个整数能否被另一个整数整除之类的问题。这两个看似相距甚远的学科，实际上从很早开始就相互影响，而且在过去的四分之一个世纪里，相互影响力大大增强。其结果是加深了对数学这两个领域的理解。 ***