OVERCONVERGENT MODULAR AND DE RHAM SHEAVES AND P-ADIC ITERATION OF THE GAUSS-MANIN CONNECTION

We construct p-adic iteration of the Gauss-Manin connection on overconvergent sheaves of de Rham classes on Hilbert modular varieties in the case p is unramified in the totally real field. This is a generalization of the work of Andreatta-Iovita in the case of elliptic curves, using a technique that marks an improvement on their approach in terms of convergence of the iterates of the connection.