LATTICES IN FILTERED (φ, N)-MODULES

Let p be a prime. We construct and study integral and torsion invariants, such as integral and torsion Weil-Deligne representations, associated to potentially semi-stable representations and torsion potentially semi-stable representations respectively. As applications, we prove the compatibility between local Langlands correspondence and Fontaine's construction for Galois representations attached to Hilbert modular forms, and Neron-Ogg-Shafarevich criterion of finite level for potentially semi-stable representations.