Patching and the -adic Langlands program for

DOI10.1112/S0010437X17007606zbMath1461.11157arXiv1609.06902OpenAlexW3109539975MaRDI QIDQ4600325

Ana Caraiani, Toby Gee, Sug Woo Shin, Matthew Emerton, Vytautas Paškūnas, David Geraghty

Publication date: 8 January 2018

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.06902

zbMATH Keywords

\(p\)-adic Langlandslocal-global compatibilityTaylor-Wiles patching

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Langlands-Weil conjectures, nonabelian class field theory (11S37)

Related Items (12)

PATCHING AND THE COMPLETED HOMOLOGY OF LOCALLY SYMMETRIC SPACES ⋮ ON SOME CONSEQUENCES OF A THEOREM OF J. LUDWIG ⋮ On the étale cohomology of Hilbert modular varieties with torsion coefficients ⋮ Zeta morphisms for rank two universal deformations ⋮ The cohomology of Shimura varieties with torsion coefficients ⋮ Towards a mod-p Lubin–Tate theory for GL2 over totally real fields ⋮ Representations of \(p\)-adic groups over commutative rings ⋮ On crystabelline deformation rings of \(\mathrm{Gal}(\overline{\mathbb {Q}}_p/\mathbb {Q}_p)\) (with an appendix by Jack Shotton) ⋮ A note on integral structures in some locally algebraic representations of \(\mathrm{GL}_2\) ⋮ On the modularity of 2-adic potentially semi-stable deformation rings ⋮ On the automorphy of 2-dimensional potentially semistable deformation rings of \(G_{\mathbb{Q}_p}\) ⋮ Diagrams in the mod p cohomology of Shimura curves

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Patching and the \(p\)-adic local Langlands correspondence
• On 2-dimensional 2-adic Galois representations of local and global fields
• The image of Colmez's Montreal functor
• A 2-adic automorphy lifting theorem for unitary groups over CM fields
• On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields
• 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 With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.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 modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Irreducible modular representations of GL\(_ 2\) of a local field
• Construction of some families of 2-dimensional crystalline representations
• Ring-theoretic properties of certain Hecke algebras
• Crystalline Dieudonné module theory via formal and rigid geometry
• On the Breuil-Mézard conjecture
• Lattices in the cohomology of Shimura curves
• Banach-Hecke algebras and \(p\)-adic Galois representations
• Potential automorphy and change of weight
• The \(p\)-adic local Langlands correspondence for \(\mathrm{GL}_2(\mathbb{Q}_p)\)
• Pseudocompact algebras, profinite groups and class formations
• The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151)
• The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
• A local proof of the Breuil–Mézard conjecture in the scalar semi‐simplification case
• Towards a modulo 𝑝 Langlands correspondence for 𝐺𝐿₂
• Completed cohomology – a survey
• The local Langlands correspondence for $GL_n$ in families
• The Fontaine-Mazur conjecture for $ {GL}_2$
• Admissible unitary completions of locally ℚ_{𝕡}-rational representations of 𝔾𝕃₂(𝔽)
• Modularity of certain potentially Barsotti-Tate Galois representations
• SUR QUELQUES REPRÉSENTATIONS MODULAIRES ET $p$-ADIQUES DE $\mathrm{GL}_2(\bm{Q}_{p})$. II
• On the p-adic cohomology of the Lubin-Tate tower
• PATCHING AND THE COMPLETED HOMOLOGY OF LOCALLY SYMMETRIC SPACES
• Potentially semi-stable deformation rings
• THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS

This page was built for publication: Patching and the -adic Langlands program for