摘要
Using p-adic local Langlands correspondence for GL 2 (Q 2 ) and an ordinary R= T theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi-stable deformation ring. This gives a new proof of the Breuil–Mézard conjecture for 2-dimensional representations of the absolute Galois group of Q 2 , which is new in the case r¯ a twist of an extension of the trivial character by itself. As a consequence, a local restriction in the proof of Fontaine-Mazur conjecture in Paškūnas (Algebra Number Theory 10(6):1301–1358, 2016) is removed.