Mathematical Sciences: Complex Multiplication of Higher-Dimensional Drinfeld Modules

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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.