The universal family of semi-stable p-adic Galois representations

Hellmann, Eugen; Hartl, Urs

Abstract

Let K be a finite field extension of Qp and let GK be its absolute Galois group. We construct the universal family of filtered (ϕ, N )-modules, or (more generally) the universal family of (ϕ, N )-modules with a Hodge-Pink lattice, and study its geometric properties. Building on this, we construct the universal family of semi-stable GK -representations in Qp-algebras. All these universal families are parametrized by moduli spaces which are Artin stacks in schemes or in adic spaces locally of finite type over Qp in the sense of Huber. This has conjectural applications to the p-adic local Langlands program.