This grant supports the research of G. Faltings with post- doctoral associates S. Zhang and J-F Burnol to work on problems in arithmetic geometry. This includes problems in etale cohomolgy, relations between modular forms and cohomology as well as moduli spaces associated to G-bundles. 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 withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.
