Wiles defect for Hecke algebras that are not complete intersections

DOI10.1112/S0010437X21007454zbMath1480.11064arXiv1910.08507OpenAlexW3195900283MaRDI QIDQ5009397

Gebhard Böckle, Jeffrey A. Manning, Chandrashekhar B. Khare

Publication date: 23 August 2021

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

Full work available at URL: https://arxiv.org/abs/1910.08507

zbMATH Keywords

Cohen-Macaulaymodularity theoremWiles defect

Mathematics Subject Classification ID

Galois representations (11F80) Theory of modules and ideals in commutative rings (13C99) Arithmetic rings and other special commutative rings (13F99)

Related Items

Independent sequences and freeness criteria, Equidimensionality of universal pseudodeformation rings in characteristic p for absolute Galois groups of p-adic fields

Cites Work

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• Patching and the \(p\)-adic local Langlands correspondence
• Local deformation rings for \(\mathrm{GL}_2\) and a Breuil-Mézard conjecture when \(l\neq p\)
• Deformations of polarized automorphic Galois representations and adjoint Selmer groups
• A family of Calabi-Yau varieties and potential automorphy. II.
• 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 With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.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
• Serre's modularity conjecture. I
• Refined conjectures of the ``Birch and Swinnerton-Dyer type
• Congruences of cusp forms and special values of their zeta functions
• On congruence divisors of cusp forms as factors of the special values of their zeta functions
• Non-optimal levels of \(\text{mod }l\) modular representations
• Lifting modular mod \(l\) representations
• The Taylor-Wiles construction and multiplicity one
• On isomorphisms between deformation rings and Hecke rings (with an Appendix by Gebhard Böckle)
• Singularities of ordinary deformation rings
• The weight in Serre's conjectures on modular forms
• On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
• Modular elliptic curves and Fermat's Last Theorem
• Lifting \(G\)-irreducible but \(\mathrm{GL}_n\)-reducible Galois representations
• Patching and multiplicity \(2^k\) for Shimura curves
• Lattices in the cohomology of Shimura curves
• The Breuil-Mézard conjecture when \(l\neq p\)
• Potential automorphy and change of weight
• On maps between modular Jacobians and Jacobians of Shimura curves
• On tensor products of Gorenstein rings
• Automorphy of some residually dihedral Galois representations
• Deformations of certain reducible Galois representations, II
• Parametrizations of elliptic curves by Shimura curves and by classical modular curves