Serre weights for quaternion algebras

DOI10.1112/S0010437X1000518XzbMath1282.11042arXiv0909.1278OpenAlexW2145474257MaRDI QIDQ5199357

David Savitt, Toby Gee

Publication date: 16 August 2011

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

Full work available at URL: https://arxiv.org/abs/0909.1278

zbMATH Keywords

quaternion algebrasGalois representationsBreuil modulesSerre weights

Mathematics Subject Classification ID

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

Related Items (9)

General Serre weight conjectures ⋮ Weight cycling and Serre-type conjectures for unitary groups ⋮ On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields ⋮ On non-abelian Lubin–Tate theory for ⋮ Potentially semi-stable deformation rings for discrete series extended types ⋮ On the weights of mod \(p\) Hilbert modular forms ⋮ The Breuil-Mézard conjecture for quaternion algebras ⋮ A classification of Breuil modules ⋮ SERRE WEIGHTS FOR LOCALLY REDUCIBLE TWO-DIMENSIONAL GALOIS REPRESENTATIONS

Cites Work

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• Moduli of finite flat group schemes, and modularity
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• Modularity of 2-adic Barsotti-Tate representations
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Lifting modular mod \(l\) representations
• Semi-stable \(p\)-adic representations and Griffiths' transversality
• Modular multiplicities and representations of \(\text{GL}_2(\mathbb Z_p)\) and \(\text{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)\) at \(\ell=p\)
• A local analysis of congruences in the \((p,p)\) case. II
• Two letters on quaternions and modular forms \(\pmod p\) (with an introduction, appendix and references by R. Livné)
• \(p\)-divisible groups, finite groups and filtered modules
• On a conjecture of Conrad, Diamond, and Taylor
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Modularity of certain potentially Barsotti-Tate Galois representations
• Modularity of some potentially Barsotti–Tate Galois representations
• Potentially semi-stable deformation rings

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