Local Langlands correspondence in rigid families

DOI10.2140/pjm.2020.304.65zbMath1476.11083arXiv1708.01213OpenAlexW2970182340WikidataQ126309789 ScholiaQ126309789MaRDI QIDQ2305475

Christian Johansson, James Newton, Claus Mazanti Sorensen

Publication date: 11 March 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.01213

zbMATH Keywords

local Langlands correspondenceGalois representationseigenvarieties\(p\)-adic automorphic forms

Mathematics Subject Classification ID

Galois representations (11F80) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Cites Work

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• Patching and the \(p\)-adic local Langlands correspondence
• Monodromy and local-global compatibility for \(l=p\)
• A modular interpretation of the trianguline variety
• Galois representations arising from some compact Shimura varieties
• A local-global compatibility conjecture in the \(p\)-adic Langlands programme for \(\text{GL}_{2}/\mathbb Q\)
• A generalization of level-raising congruences for algebraic modular forms
• Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.
• On the conductors of mod \(\ell\) Galois representations coming from modular forms
• Conducteur des représentations du groupe linéaire
• Irreducible components of rigid spaces
• Algebras of \(p\)-adic distributions and admissible representations
• Iwahori component of the Gelfand-Graev representation
• Base change and a problem of Serre
• The Langlands-Kottwitz approach for some simple Shimura varieties
• The local Langlands correspondence for \(\mathrm{GL}_n\) over \(p\)-adic fields
• Ordinary representations of \(G(\mathbb{Q}_p)\) and fundamental algebraic representations
• Strong local-global compatibility in the \(p\)-adic Langlands program for \(U(2)\)
• Universal eigenvarieties, trianguline Galois representations, and \(p\)-adic Langlands functoriality
• Local-global compatibility for \(l=p\). I
• On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms
• On extensions of generalized Steinberg representations
• The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151)
• Equations differentielles p-adiques et modules de Jacquet analytiques
• The local Langlands correspondence for $GL_n$ in families
• p-Adic Lie Groups
• Overconvergent algebraic automorphic forms
• The Langlands-Kottwitz approach for the modular curve
• The sign of Galois representations attached to automorphic forms for unitary groups
• Local to global compatibility on the eigencurve
• 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
• Compatibility of local and global Langlands correspondences
• Jacquet modules of locally analytic representations of p-adic reductive groups I. Construction and first properties
• Extensions for supersingular representations of $GL_2(Q_p)$
• Der erste Riemannsche Hebbarkeitssatz im nichtarchimedischen Fall.
• Induced representations of reductive ${\germ p}$-adic groups. I
• A note on Jacquet functors and ordinary parts
• INJECTIVITY, PROJECTIVITY AND SUPERCUSPIDAL REPRESENTATIONS
• Familles p-adiques de formes automorphes pour GLn
• Bernstein–Zelevinsky Derivatives: a Hecke Algebra Approach
• Endoscopic Classification of representations of Quasi-Split Unitary Groups
• Locally analytic vectors in representations of locally 𝑝-adic analytic groups
• On the infinite fern of Galois representations of unitary type
• Local-global compatibility for $l=p$, II