Ihara's lemma for Shimura curves over totally real fields via patching

DOI10.1007/s00208-020-02048-8zbMath1472.11170arXiv1907.06043OpenAlexW3088532389WikidataQ124989446 ScholiaQ124989446MaRDI QIDQ2225607

Jack Shotton, Jeffrey A. Manning

Publication date: 8 February 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.06043

zbMATH Keywords

Shimura curveHecke algebraTaylor-Wiles methodIhara's Lemma

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items (8)

Arithmetic of Shimura varieties. Abstracts from the workshop held January 29 -- February 4, 2023 ⋮ Gelfand-Kirillov dimension and the \(p\)-adic Jacquet-Langlands correspondence ⋮ Iwasawa theory of Hilbert modular forms for anticyclotomic extensions without Ihara's lemma ⋮ INDIVISIBILITY OF HEEGNER CYCLES OVER SHIMURA CURVES AND SELMER GROUPS ⋮ On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights ⋮ On the Bloch-Kato conjecture for Hilbert modular forms ⋮ A proof of Perrin-Riou's Heegner point main conjecture ⋮ The universal unramified module for \(\mathrm{GL}(n)\) and the Ihara conjecture

Cites Work

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• Local deformation rings for \(\mathrm{GL}_2\) and a Breuil-Mézard conjecture when \(l\neq p\)
• Anticyclotomic Iwasawa's main conjecture for Hilbert modular forms
• Automorphic lifts of prescribed types
• On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields
• Iwasawa's main conjecture for elliptic curves over anticyclotonic \(\mathbb Z_p\)-extensions
• On Galois representations associated to Hilbert modular forms
• Moduli of finite flat group schemes, and modularity
• 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 With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.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
• Non-optimal levels of \(\text{mod }l\) modular representations
• Lifting modular mod \(l\) representations
• The Taylor-Wiles construction and multiplicity one
• Modularity lifting beyond the Taylor-Wiles method
• The weight in Serre's conjectures on modular forms
• On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
• Reduction modulo P of Shimura curves
• Lattices in the cohomology of Shimura curves
• Strong local-global compatibility in the \(p\)-adic Langlands program for \(U(2)\)
• On the meromorphic continuation of degree two \(L\)-functions
• The Breuil-Mézard conjecture when \(l\neq p\)
• Potential automorphy and change of weight
• The local Langlands correspondence for $GL_n$ in families
• Formes modulaires de Hilbert modulo $p$ et valeurs d'extensions entre caractères galoisiens
• On the Schur Indices of Characters of Finite Classical Groups
• On the p-adic cohomology of the Lubin-Tate tower
• THE WEIGHT PART OF SERRE’S CONJECTURE FOR
• On the anticyclotomic Iwasawa main conjecture for modular forms
• Potentially semi-stable deformation rings

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