Shimura curves, mod p de Rham cohomology and Serre weights

I will discuss joint work with Teruyoshi Yoshida in which we
investigate the mod p Galois representations associated to Hilbert
modular forms by studying mod p de Rham cohomology groups of integral
models for Shimura curves. This has applications to generalised Serre
weight conjectures (conjectures first made by Michael Schein in our
context), and suggests some questions about the structure of finite
flat group schemes appearing in the Picard scheme of the integral
models under consideration.