Congruences between Hilbert modular forms: constructing ordinary lifts

DOI10.1215/00127094-1593326zbMath1297.11028arXiv1006.0466OpenAlexW2963783415MaRDI QIDQ431557

Toby Gee, Thomas Barnet-Lamb, David Geraghty

Publication date: 28 June 2012

Published in: Mathematical Research Letters, Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.0466

zbMATH Keywords

Hilbert modular forms\(p\)-adic modular formsBarsotti-Tate representationsBuzzard-Diamond-Jarvis conjecturemodularity lifting theorems

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (26)

Serre weights for rank two unitary groups ⋮ On mod local-global compatibility for in the ordinary case ⋮ A Serre weight conjecture for geometric Hilbert modular forms in characteristic \(p\) ⋮ Elliptic curves and modularity ⋮ Elliptic curves over totally real cubic fields are modular ⋮ Langlands base change for \(\mathrm{GL}(2)\) ⋮ Potential automorphy and change of weight ⋮ Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms ⋮ Irreducibility of automorphic Galois representations of \(\mathrm{GL}(n)\), \(n\) at most \(5\) ⋮ A geometric perspective on the Breuil–Mézard conjecture ⋮ On Serre's uniformity conjecture for semistable elliptic curves over totally real fields ⋮ The Buzzard–Diamond–Jarvis conjecture for unitary groups ⋮ A 2-adic automorphy lifting theorem for unitary groups over CM fields ⋮ Serre weights for \(\mathrm{U}(n)\) ⋮ Modularity lifting in parallel weight one ⋮ Automorphy of some residually \(S_5\) Galois representations ⋮ Elliptic curves over real quadratic fields are modular ⋮ Abelian surfaces over totally real fields are potentially modular ⋮ THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS ⋮ Companion forms in parallel weight one ⋮ Automorphy lifting for residually reducible 𝑙-adic Galois representations ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\) ⋮ Lattices in the cohomology of Shimura curves ⋮ Lifting and automorphy of reducible mod \(p\) Galois representations over global fields ⋮ Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case ⋮ \(p\)-adic Hilbert modular forms of weight 1

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