Local deformation rings for GL2 and a Breuil-Mezard conjecture when l ≠ p

We compute the deformation rings of two dimensional mod l representations of Gal((F) over bar /F) with fixed inertial type for l an odd prime, p a prime distinct from l, and F = Q(p) a finite extension. We show that in this setting an analogue of the Breuil-Mezard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL(2) (O-F).