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 étale (φ, Γ)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogs, for not necessarily étale (φ, Γ)-modules over the Robba ring, of the Euler–Poincaré characteristic formula and Tate local duality for p-adic representations. These results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations.