This award supports research centered on Iwasawa theory and special values of Hecke L-functions. This project involves work on three questions regarding these special values, the first two of which are concerned with the conjectures made by Beilinson and Bloch-Kato. These conjectures reveal an intrinsic connection between the special values of a motivic L-function and the arithmetic properties of the motive. The first part of this research deals with the Bloch-Kato conjecture at critical values of Hecke L-functions from CM elliptic curves. The second part addresses the Beilinson conjecture at the central critical values of Hecke L-functions. The third part explores a possible duality property in Iwasawa theory induced by the generalized Tate duality for p-adic Galois representations. 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.
