On the weights of mod pp Hilbert modular forms

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod $p$ Hilbert modular forms, by making use of modularity lifting theorems and computations in $p$-adic Hodge theory.Comment: 34 pages. Essentially final version, to appear in Inventiones mathematicae. This version does not incorporate any minor changes (e.g. typographical changes) made in proo

Explicit reduction modulo pp of certain crystalline representations

We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms.Comment: 10 pages, appeared in IMRN 2009, no. 12. This version does not incorporate any minor changes (e.g. typographical changes) made in proo

Explicit reduction modulo p of certain 2-dimensional crystalline representations, II

We complete the calculations begun in [BG09], using the p-adic local Langlands correspondence for GL2(Q_p) to give a complete description of the reduction modulo p of the 2-dimensional crystalline representations of G_{Q_p} of slope less than 1, when p > 2.Comment: 10 pages. Correcting a minor typ