Arthur Ogus

Conjectures of Gouvea and Mazur motivate the construction of cohomology groups over ${\bf Z}_p$ associated to modular forms of high weight. Most of these constructions seem to produce groups containsing torsion and other ``pathologies,'' but in 1985 Tony Scholl showed how to construct De Rham cohomology groups which are torsion free and autodual. However, the Hodge and conjugate spectral sequences associated to the Frobenius action on these groups do not degenerate, and consequently the calculation of the associated Hodge numbers (in the sense of Mazur) seems to require some new techniques.