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. ***

约旦这个奖项为布鲁斯·约旦教授的研究资助了Shimura品种的Hecke结构。 晶体共同体学的最新进展使得控制惯性对品种的P-ADIC共同学组的作用对未受到的扩展，并且对合理的P-ADIC领域的降低良好。 约旦教授希望将这些技术应用于Shimura品种。 这是算术代数几何学领域的研究，该几何形状结合了代数几何学和数字理论的技术。在其原始配方中，代数几何处理的数字可以通过最简单的方程式在平面上定义的数字，即多项式。数字理论始于整个数字，以及一个总数诸如另一个数字的分裂性。实际上，这两个主题似乎相距甚远，实际上已经从最早的时候互相影响，但是在过去的四分之一世纪中，相互影响的影响很大。结果是对两个数学领域的了解都在越来越多。 ***