A Serre weight conjecture for geometric Hilbert modular forms in characteristic \(p\)

DOI10.4171/jems/1265arXiv1712.03775OpenAlexW2771769606WikidataQ123366243 ScholiaQ123366243MaRDI QIDQ6057870

Fred Diamond, Shu Sasaki

Publication date: 26 October 2023

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03775

zbMATH Keywords

Hilbert modular formsSerre's conjecture

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Congruences between Hilbert modular forms: constructing ordinary lifts
• Galois representations and torsion in the coherent cohomology of Hilbert modular varieties
• Automorphic lifts of prescribed types
• On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields
• Higher Koecher's principle
• \(p\)-adic \(L\)-functions for CM fields
• A modularity lifting theorem for weight two Hilbert modular forms
• On Galois representations associated to Hilbert modular forms
• Weights in Serre's conjecture for Hilbert modular forms: the ramified case
• Moduli of finite flat group schemes, and modularity
• Serre's modularity conjecture. I
• Serre's modularity conjecture. II
• Modularity of 2-adic Barsotti-Tate representations
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Companion forms and Kodaira-Spencer theory
• Modular multiplicities and representations of \(\text{GL}_2(\mathbb Z_p)\) and \(\text{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)\) at \(\ell=p\)
• Grothendieck duality and base change
• General Serre weight conjectures
• Modularity lifting beyond the Taylor-Wiles method
• Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms
• Local models in the ramified case. II: Splitting models
• The weight in Serre's conjectures on modular forms
• Appendix to ``The Iwasawa conjecture for totally real fields by A.Wiles: Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces
• A tameness criterion for Galois representations associated to modular forms (mod \(p\))
• An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the \(\operatorname{mod} p\) cohomology of \(\text{GL}(n,\mathbb{Z})\)
• \(l\)-modular representations of a \(p\)-adic reductive group with \(l\neq p\)
• Automorphy of some residually \(S_5\) Galois representations
• Strata Hasse invariants, Hecke algebras and Galois representations
• A note on the \(p\)-adic Galois representations attached to Hilbert modular forms
• Companion forms in parallel weight one
• SERRE WEIGHTS AND WILD RAMIFICATION IN TWO-DIMENSIONAL GALOIS REPRESENTATIONS
• Extensions of rank one (φ,Γ)-modules and crystalline representations
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Construction de représentations $p$-adiques
• UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES
• Hilbert modular forms: mod 𝑝 and 𝑝-adic aspects
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
• UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD  OF WEIGHT 1
• Minimal weights of Hilbert modular forms in characteristic
• Explicit Serre weights for two-dimensional Galois representations
• The Buzzard–Diamond–Jarvis conjecture for unitary groups
• Serre weights and Shimura curves
• THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS
• A mod $p$ Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties: Splicing and dicing

This page was built for publication: A Serre weight conjecture for geometric Hilbert modular forms in characteristic \(p\)