Vol. 14, No. 5, 2020

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The universal family of semistable $p$-adic Galois representations

Urs Hartl and Eugen Hellmann

Vol. 14 (2020), No. 5, 1055–1121

Let K be a finite field extension of p 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 semistable 𝒢K-representations in p-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 p in the sense of Huber. This has conjectural applications to the p-adic local Langlands program.

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p-adic Galois representations, crystalline representations, semistable representations, moduli spaces, filtered modules
Mathematical Subject Classification 2010
Primary: 11S20
Secondary: 11F80, 13A35
Received: 8 October 2015
Revised: 29 May 2019
Accepted: 24 November 2019
Published: 13 July 2020
Urs Hartl
Mathematisches Institut
Universität Münster
Eugen Hellmann
Mathematisches Institut
Universität Münster