Potentially crystalline deformation rings and Serre weight conjectures: shapes and shadows

DOI10.1007/s00222-017-0762-0zbMath1403.11039arXiv1512.06380OpenAlexW2765721587WikidataQ122874589 ScholiaQ122874589MaRDI QIDQ1745390

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

Publication date: 17 April 2018

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

Full work available at URL: https://arxiv.org/abs/1512.06380

zbMATH Keywords

Galois cohomologyHodge-Tate weightsKisin modulesBreuil-Mézard conjecturescrystalline deformation ringsSerre weight conjectures

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80)

Related Items

Connectedness of Kisin varieties associated to absolutely irreducible Galois representations ⋮ From p-modular to p-adic Langlands Correspondences for $${\mathrm {U}(1,1)({\mathbb {Q}_{{p}^{2}}}/\mathbb {Q}_{p})}$$ : Deformations in the Non-supercuspidal Case ⋮ General Serre weight conjectures ⋮ Crystalline liftings and the weight part of Serre's conjecture ⋮ On the mod \(p\) cohomology for \(\mathrm{GL}_2\) ⋮ On mod local-global compatibility for in the ordinary case ⋮ Gelfand-Kirillov dimension and mod \(p\) cohomology for \(\mathrm{GL}_2 \) ⋮ Can We Dream of a 1-Adic Langlands Correspondence? ⋮ G-valued crystalline deformation rings in the Fontaine–Laffaille range ⋮ Local models for Galois deformation rings and applications ⋮ Potentially diagonalisable lifts with controlled Hodge-Tate weights ⋮ Potentially crystalline deformation rings in the ordinary case ⋮ SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE ⋮ Multiplicity one for wildly ramified representations ⋮ 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

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