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

该奖项资助了Bruce Jordan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在有理p进域上具有良好约简的非分枝扩展上控制惯性对变异的p进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。在其最初的公式中，代数几何处理的图形可以用最简单的方程，即多项式在平面上定义。数论始于整数和整数能否被整数整除之类的问题。这两个看似相距甚远的主题，实际上从最早的时代起就相互影响，但在过去的四分之一世纪中，相互影响大大增加。其结果是加深了对这两个数学领域的理解。＊＊＊

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. ***