We compute the deformation rings of two dimensional mod l rep- resentations of Gal(F/F) with fixed inertial type, for l an odd prime, p a prime distinct from l, and F/Qp a finite extension. We show that in this set- ting an analogue of the Breuil–M´ezard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL2(OF ).
Shotton, J. (2016). Local deformation rings for GL2 and a Breuil–Mézard conjecture when l≠p. Algebra & Number Theory, 10(7), 1437-1475. https://doi.org/10.2140/ant.2016.10.1437