Adrian Ioviţă
Concordia University, Montreal, Canada & University of Padova, Italy

Given a $p$-adic weight, one has a sheaf of Banach modules with integrable connection and filtration, on a strict neighbourhood of the ordinary locus in an appropriate modular curve. The de Rham cohomology of this module with connection can be calculated in terms of overconvergent modular forms of various weights, using the local action of the Lie-algebra $sl_2$ on this sheaf, in a way similar to the classical Bernstein-Gelfand-Gelfand method (for short BGG).