Abstract
Using the p-adic local Langlands correspondence for GL <sub>2</sub> (Q <sub>p</sub> ), we prove that the support of the patched modules M <sub>∞</sub> (σ)[1/p] constructed by Caraiani et al. (Compos. Math. 154:3 (2018), 503–548) meets every irreducible component of the potentially semistable deformation ring R <sup>□</sup> <sub>r</sub> (σ)[1/p]. This gives a new proof of the Breuil–Mézard conjecture for 2-dimensional representations of the absolute Galois group of Q <sub>p</sub> when p > 2, which is new for p = 3 and ¯r a twist of an extension of the trivial character by the mod p cyclotomic character. As a consequence, a local restriction in the proof of the Fontaine–Mazur conjecture by Kisin (J. Amer. Math. Soc. 22:3 (2009), 641–690) is removed.