On the weights of mod $p$ Hilbert modular forms

Abstract

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.

34 pages. Essentially final version, to appear in Inventiones mathematicae. This version does not incorporate any minor changes (e.g. typographical changes) made in proof