Cohomology and duality for (φ,Γ)-modules over the Robba ring

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (φ,Γ)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily etale (φ,Γ)-modules over the Robba ring, of the Euler-Poincare characteristic formula and Tate local duality for p-adic representations.