Mathematical Sciences: Selmer Groups and Iwasawa Theory

点击翻译按钮获取中文摘要

Professor Greenberg will continue his work on several problems connected with a generalized Iwasawa theory. He will study Selmer groups associated to abelian varieties and to certain families of p-adic representations. Greenberg will also investigate the phenomenon of trivial zeros of p-adic L-functions in an attempt to understand more fully the corresponding derivatives of these functions. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful, having recently solved problems that have withstood generations. Among its many consequences are new error-correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.