The Fontaine-Mazur conjecture in the residually reducible case

DOI10.1090/jams/991zbMath1502.11062arXiv1901.07166OpenAlexW2909942499WikidataQ113823096 ScholiaQ113823096MaRDI QIDQ5096123

Lue Pan

Publication date: 15 August 2022

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.07166

zbMATH Keywords

Galois representationsFontaine-Mazur conjectureHecke algebraHida family\(p\)-adic local Langlands correspondencelocal-global compatibilitypseudo-representationsGalois deformation ring

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11) Galois representations (11F80) Representations of Lie and linear algebraic groups over local fields (22E50) Langlands-Weil conjectures, nonabelian class field theory (11R39)

Related Items (10)

Modularity lifting theorems ⋮ 𝑅=𝑇 theorems for weight one modular forms ⋮ On the étale cohomology of Hilbert modular varieties with torsion coefficients ⋮ Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$ ⋮ \(\mathbb{Q}\)-curves, Hecke characters, and some Diophantine equations. II ⋮ Gelfand-Kirillov dimension and the \(p\)-adic Jacquet-Langlands correspondence ⋮ On the images of Galois representations attached to low weight Siegel modular forms ⋮ A simplified proof of Serre's conjecture ⋮ Adjoint Selmer groups of automorphic Galois representations of unitary type ⋮ Congruences between modular forms

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