Strong local-global compatibility in the p-adic Langlands program for   U(2)
  We prove that certain Galois-isotypic parts of the completed cohomology group for U(2) can be written as a completed tensor product of a representation coming from the p-adic Langlands correspondence for $GL_2(\mathbb{Q}_p)$ and a representation arising via the local Langlands correspondence in famillies of Emerton and Helm. 
Przemyslaw Chojecki, Claus Sorensen
math.NT