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2020 The universal family of semistable $p$-adic Galois representations
Urs Hartl, Eugen Hellmann
Algebra Number Theory 14(5): 1055-1121 (2020). DOI: 10.2140/ant.2020.14.1055

Abstract

Let K be a finite field extension of p and let 𝒢 K 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 𝒢 K -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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Urs Hartl. Eugen Hellmann. "The universal family of semistable $p$-adic Galois representations." Algebra Number Theory 14 (5) 1055 - 1121, 2020. https://doi.org/10.2140/ant.2020.14.1055

Information

Received: 8 October 2015; Revised: 29 May 2019; Accepted: 24 November 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07244791
MathSciNet: MR4129383
Digital Object Identifier: 10.2140/ant.2020.14.1055

Subjects:
Primary: 11S20
Secondary: 11F80 , 13A35

Keywords: crystalline representations , filtered modules , moduli spaces , p-adic Galois representations , semistable representations

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 5 • 2020
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