Mathematical Sciences: Complex Multiplication of Higher-Dimensional Drinfeld Modules

首席研究员的项目是开发一条互易律，控制Drinfeld模的高维类似物上扭点的行为；他称之为Abelian A-模。其结果之一是在每个具有复数乘法的阿贝尔A-模上附加一个Hecke特征标，并在Goss的工作基础上发展了附加于这些特征标的L级数理论。本研究是在有限特征的代数几何中进行的。虽然这个领域起源于像线和面这样不断变化的几何结构的概念，但在这种情况下，离散的概念占据了主导地位，类似于整数理论的方法是最有用的。反过来，有限特征的代数几何现在对数论产生了很大的影响，并在计算机科学和编码理论中得到了应用。

The Principal Investigator's project is to develop a reciprocity law governing the behavior of torsion points on higher-dimensional analogues of Drinfeld modules; he calls these Abelian A-modules. One of the products of this would be to attach a Hecke character to each Abelian A-module with complex multiplication, and develop the theory of L-series attached to such characters, following the work of Goss. This research is work in the Algebraic Geometry of finite characteristic. Although the field originated with notions of continuously varying geometric structures like lines and planes, in this context the Discrete takes over, and methods akin to those from the theory of whole numbers are most useful. Reciprocally, the algebraic geometry of finite characteristic is now having great influence on the Theory of Numbers, and is finding application in Computer Science and Coding Theory.