The universal family of semistable p-adic Galois representations

2013/12/31 by Urs Hartl, Eugen Hellmann · 13 citations
Mathematics · #Absolute Galois group #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebra over a field #Algebraic Geometry and Number Theory #Discrete mathematics #Galois group #Galois module #Mathematics #Moduli space #Pure mathematics #math.AG #math.NT #msc:11S20

paper · pdf · doi:10.2140/ant.2020.14.1055

published in Algebra & Number Theory 14(5), 1055-1121 (Mathematical Sciences Publishers) · final version, to appear in ANT

arxiv created 2020/01/16 · openalex publication_date 2020/07/13 · arxiv updated 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let [math] be a finite field extension of [math] and let [math] be its absolute Galois group. We construct the universal family of filtered [math] -modules, or (more generally) the universal family of [math] -modules with a Hodge–Pink lattice, and study its geometric properties. Building on this, we construct the universal family of semistable [math] -representations in [math] -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 [math] in the sense of Huber. This has conjectural applications to the [math] -adic local Langlands program.

Citations

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