  In 1987 Serre conjectured that any mod l ("ell", not "1") two-dimensional
irreducible odd representation of the absolute Galois group of the rationals
came from a modular form in a precise way. We present a generalisation of this
conjecture to 2-dimensional representations of the absolute Galois group of a
totally real field where l is unramified. The hard work is in formulating an
analogue of the "weight" part of Serre's conjecture. Serre furthermore asked
whether his conjecture could be rephrased in terms of a "mod l Langlands
philosophy". Using ideas of Emerton and Vigneras, we formulate a mod l
local-global principle for the group D^*, where D is a quaternion algebra over
a totally real field, split above l and at 0 or 1 infinite places, and show how
it implies the conjecture.
