SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE

DOI10.1017/fmp.2020.1zbMath1452.11066arXiv1608.06570OpenAlexW3013821105WikidataQ122964091 ScholiaQ122964091MaRDI QIDQ5221063

Daniel Le, Bao V. Le Hung, Brandon Levin, Stefano Morra

Publication date: 27 March 2020

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.06570

zbMATH Keywords

Galois representationBreuil's lattice conjecture

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) Representations of finite groups of Lie type (20C33)

Related Items (12)

Connectedness of Kisin varieties associated to absolutely irreducible Galois representations ⋮ MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL ⋮ On the mod \(p\) cohomology for \(\mathrm{GL}_2\) ⋮ Non-admissible irreducible representations of 𝑝-adic 𝐺𝐿_{𝑛} in characteristic 𝑝 ⋮ Gelfand-Kirillov dimension and mod \(p\) cohomology for \(\mathrm{GL}_2 \) ⋮ Can We Dream of a 1-Adic Langlands Correspondence? ⋮ Local models for Galois deformation rings and applications ⋮ Combinatorics of Serre weights in the potentially Barsotti-Tate setting ⋮ Potentially crystalline deformation rings and Serre weight conjectures: shapes and shadows ⋮ Diagrams in the mod p cohomology of Shimura curves ⋮ Weight elimination in Serre-type conjectures ⋮ Serre weight conjectures for \(p\)-adic unitary groups of rank 2

Cites Work

• Unnamed Item
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• Patching and the \(p\)-adic local Langlands correspondence
• Weight cycling and Serre-type conjectures for unitary groups
• Automorphic lifts of prescribed types
• Extensions of simple modules for finite Chevalley groups
• 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 With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.
• Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. II
• Representations of reductive groups over finite fields
• Reduction modulo \(p\) of some Deligne-Lusztig characters
• Loewy series for principal series representations of finite Chevalley groups
• The Taylor-Wiles construction and multiplicity one
• General Serre weight conjectures
• Non-minimal modularity lifting in weight one
• Potentially crystalline deformation rings and Serre weight conjectures: shapes and shadows
• Lattices in the cohomology of \(U(3)\) arithmetic manifolds
• On weight elimination for \(\mathrm{GL}_n (\mathbb{Q}_{p^f})\)
• The weight in a Serre-type conjecture for tame \(n\)-dimensional Galois representations
• Weight elimination in Serre-type conjectures
• Lattices in the cohomology of Shimura curves
• On a problem of local-global compatibility modulo \(p\) for \(\mathrm{GL}_2\) (with an Appendix of Lassina Dembélé)
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• Filtrations on G ₁ T -Modules
• Towards a modulo 𝑝 Langlands correspondence for 𝐺𝐿₂
• Modularity of certain potentially Barsotti-Tate Galois representations
• On mod local-global compatibility for in the ordinary case
• Kisin modules with descent data and parahoric local models
• Reflexive pull-backs and base extension
• DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE
• Modularity lifting theorems for Galois representations of unitary type
• A geometric perspective on the Breuil–Mézard conjecture
• Potentially semi-stable deformation rings

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