Admissible φ-modules and p-adic unitary representations

Abstract

Generalizing results of J.-M. Fontaine and A. Scholl, we describe the p-adic unitary not necessarily finite dimensional representations of the absolute Galois group of certain fields in terms of admissible φ-modules and admissible (φ, Γ)-modules. If K is a nonarchimedean local field and if h ≥ 1 is an integer then several prominent compact subgroups of GL h (K) appear as quotients of these Galois groups. This allows us to give a functorial description of their p-adic unitary representations in terms of admissible φ-modules and admissible (φ, Γ)-modules over certain coefficient rings.