On the Colmez functor from GL(2,Q_p) to (phi,Gamma)-modules

Let O_L be the ring of integers of a finite extension L/Q_p. We will explain how any finite length smooth O_L representation of G=GL(2,Q_p) with a central character is the 0-th homology of a G-equivariant coefficient system on the tree, recall (quickly) the definition of the Colmez functor and discuss a generalisation to GL(n,Q_p) suggested by Schneider.