This research is in several areas of algebraic geometry and number theory. Hartshorne will pursue various questions concerning the classification of algebraic vector bundles and reflexive sheaves on projective spaces. Ogus will continue his work on crystalline cohomology of algebraic varieties in characteristic p. Ribet will work on several aspects of arithmetic algebraic geometry. Coleman will continue his work on p-adic integrals with applications to arithmetical algebraic geometry. The topics intellectually connected together as they are make for a research program greater than the sum of the parts.
