Smoothness and classicality on eigenvarieties

DOI10.1007/s00222-016-0708-yzbMath1410.11042arXiv1510.01222OpenAlexW2963958470MaRDI QIDQ2406817

Eugen Hellmann, Christophe Breuil, Benjamin Schraen

Publication date: 6 October 2017

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01222

zbMATH Keywords

Galois representationeigenvarietyoverconvergent \(p\)-adic automorphic form

Mathematics Subject Classification ID

(p)-adic theory, local fields (11F85) Galois representations (11F80) Class field theory; (p)-adic formal groups (11S31)

Related Items

Companion points and locally analytic socle for \(\mathrm{GL}_2(L)\), Tangent spaces on the trianguline variety at companion points, A note on critical \(p\)-adic \(L\)-functions, A modular interpretation of the trianguline variety, Smoothness of definite unitary eigenvarieties at critical points, Simple ℒ-invariants for GL_{𝓃}, Density of automorphic points in deformation rings of polarized global Galois representations, A local model for the trianguline variety and applications

Cites Work

• Unnamed Item
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• Patching and the \(p\)-adic local Langlands correspondence
• Locally analytic socle. I.
• Weight cycling and Serre-type conjectures for unitary groups
• Universal completions for representations of \(\mathrm{GL}_2(\mathbb{Q}_p)\)
• A modular interpretation of the trianguline variety
• Local-global compatibility and the action of monodromy on nearby cycles
• Completely continuous endomorphisms of \(p\)-adic Banach spaces
• Invariant distributions on \(p\)-adic analytic groups
• Triangulation of refined families
• Nonsmooth classical points on eigenvarieties
• Moduli of finite flat group schemes, and modularity
• Algebras of \(p\)-adic distributions and admissible representations
• Overconvergent modular forms and the Fontaine-Mazur conjecture
• \(p\)-adic representations and differential equations
• On endoscopic \(p\)-adic automorphic forms for \(\mathrm{SL}_2\)
• Crystalline Dieudonné module theory via formal and rigid geometry
• Smoothness of definite unitary eigenvarieties at critical points
• Towards the locally analytical socle for \(\mathrm{GL}_n\). II
• About the density of \(\text{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)\) crystalline representations
• Lectures on formal and rigid geometry
• Potential automorphy and change of weight
• On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Première partie). Rédigé avec la colloboration de J. Dieudonné
• Cohomology of arithmetic families of (𝜑,Γ)-modules
• A generalization of Greenberg's <i>L</i>-invariant
• On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne
• Classification of two-dimensional split trianguline representations ofp-adic fields
• Jacquet modules of locally analytic representations of p-adic reductive groups I. Construction and first properties
• Familles p-adiques de formes automorphes pour GLn
• Density of potentially crystalline representations of fixed weight
• Paraboline variation over -adic families of -modules
• On the infinite fern of Galois representations of unitary type
• Potentially semi-stable deformation rings
• On Jordan-Hölder series of some locally analytic representations
• Cohomology and Duality for (φ, Γ)-modules over the Robba Ring