Generic local deformation rings when $l\ne p$

Abstract

We determine the local deformation rings of sufficiently generic mod $l$ representations of the Galois group of a $p$-adic field, when $l\ne p$, relating them to the space of $q$-power-stable semisimple conjugacy classes in the dual group. As a consequence we give a local proof of the $l\ne p$ Breuil--Mézard conjecture of the author, in the tame case.

28 pages. Comments welcome!

Cited by in corpus (1)

• Irreducible components of the moduli space of Langlands parameters