Vol. 14, No. 5, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 8, 1865–2122
Issue 7, 1593–1864
Issue 6, 1343–1592
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
The universal family of semistable $p$-adic Galois representations

Urs Hartl and Eugen Hellmann

Vol. 14 (2020), No. 5, 1055–1121
Abstract

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.

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