Extensions of rank one (φ,Γ)-modules and crystalline representations

Abstract

Let K be a finite unramified extension of Q p. We parametrize the (φ,Γ)-modules corresponding to reducible two-dimensional F̄ p-representations of G K and characterize those which have reducible crystalline lifts with certain Hodge-Tate weights. © Copyright Foundation Compositio Mathematica 2010.