Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

2015/01/31 by Carl Wang-Erickson · 29 citations
Mathematics · #Absolute Galois group #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Embedding problem #Galois cohomology #Galois extension #Galois group #Galois module #Group (periodic table) #Mathematical analysis #Mathematics #Moduli #Moduli space #Morphism #Profinite group #Pure mathematics #Splitting of prime ideals in Galois extensions #math.AG #math.NT #msc:11F80 #msc:11S20 #msc:14D15 #msc:14L24

paper · pdf · doi:10.1007/s00208-017-1557-8

published in Mathematische Annalen 371(3-4), 1615-1681 (Springer Nature) · Numbering changed and typos corrected to match published version. 59 pages

openalex publication_date 2017/07/24 · arxiv created 2017/09/07 · arxiv updated 2018/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We construct and study the moduli of continuous representations of a profinite group with integral p -adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is algebraizable. When this profinite group is the absolute Galois group of a p -adic local field, we show that these moduli spaces admit Zariski-closed loci cutting out Galois representations that are potentially semi-stable with bounded Hodge–Tate weights and a given Hodge and Galois type. As a consequence, we show that these loci descend to the universal deformation ring of the corresponding pseudorepresentation.

Citations

• On ordinary ?-adic representations associated to modular forms
• Caractérisation des caractères et Pseudo-caractères
• A formal inverse to the Cayley-Hamilton theorem
• Pseudo-repr�sentations

Cited by

• On the automorphy of 2-dimensional potentially semi-stable deformation rings of G_ℚp
• Factorisation de la cohomologie de systèmes locaux p-adiques sur le demi-plan de Drinfeld
• The Chabauty-Kim Method for Relative Completions
• Finiteness properties of the category of mod p representations of GL₂(ℚ_p)
• Deformations of pseudocharacters and Mazur's finiteness condition
• Infinitesimal characters and Lafforgue's pseudocharacters
• The rank of Mazur’s Eisenstein ideal
• The universal family of semistable p-adic Galois representations

Related

• Moduli of p-adic representations of a profinite group
• The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
• Semi-simplified modulo p of semi-stable representations: an algorithmic approach
• Quasi-semi-stable representations
• Analyse p-adique et représentations Galoisiennes