Reciprocity in the Langlands program since Fermat's last theorem

DOI10.4171/icm2022/101arXiv2109.14145OpenAlexW3204963297MaRDI QIDQ6118163

Publication date: 20 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.14145

zbMATH Keywords

Galois representations Langlands program modularity lifting

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) Langlands-Weil conjectures, nonabelian class field theory (11S37) Cohomology of arithmetic groups (11F75)

Cites Work

Deformations of polarized automorphic Galois representations and adjoint Selmer groups
On the rigid cohomology of certain Shimura varieties
The image of Colmez's Montreal functor
Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties
The image of complex conjugation in $l$-adic representations associated to automorphic forms
On Galois representations of weight one
Monodromy and local-global compatibility for $l=p$
Level raising and symmetric power functoriality. II
Automorphy of $\mathrm{Symm}^5(\mathrm{GL}(2))$ and base change
Level-raising and symmetric power functoriality. III.
A family of Calabi-Yau varieties and potential automorphy. II.
Automorphic lifts of prescribed types
Even Galois representations and the Fontaine-Mazur conjecture
Galois representations arising from some compact Shimura varieties
$l$-adic representations associated to modular forms over imaginary quadratic fields. I: Lifting to $GSp_ 4(\mathbb{Q})$
Local-global compatibility and the action of monodromy on nearby cycles
Higher coherent cohomology and $p$-adic modular forms of singular weights
Serre's modularity conjecture: the level one case
On torsion in the cohomology of locally symmetric varieties
Moduli of finite flat group schemes, and modularity
A family of Calabi-Yau varieties and potential automorphy
The fundamental lemma for Lie algebras
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 With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.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
Serre's modularity conjecture. II
Modularity of 2-adic Barsotti-Tate representations
Galois representations into $\text{GL}_2(\mathbb Z_p X)$ attached to ordinary cusp forms.
On the modular representations of degree two of $\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})$
On ordinary $\lambda$-adic representations associated to modular forms
Représentations galoisiennes associées aux représentations automorphes autoduales de $GL(n)$. (Galois representations associated with self-dual automorphic representations of $GL(n)$)
Galois representations attached to mod $p$ cohomology of $GL(n,\mathbb{Z})$
On the $\lambda$-adic representations associated to some simple Shimura varieties
Icosahedral Galois representations
$p$-adic étale cohomology and crystalline cohomology in the semi-stable reduction case
Companion forms and weight one forms
$l$-adic representations associated to modular forms over imaginary quadratic fields. II
The Taylor-Wiles construction and multiplicity one
Modular forms and $p$-adic Hodge theory
Modular multiplicities and representations of $\text{GL}_2(\mathbb Z_p)$ and $\text{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)$ at $\ell=p$
Overconvergent modular forms and the Fontaine-Mazur conjecture
Residually reducible representations and modular forms
Nearly ordinary deformations of irreducible residual representations
On the generic part of the cohomology of compact unitary Shimura varieties
Modularity lifting beyond the Taylor-Wiles method
Derived Galois deformation rings
Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms
On crystabelline deformation rings of $\mathrm{Gal}(\overline{\mathbb {Q}}_p/\mathbb {Q}_p)$ (with an appendix by Jack Shotton)
Singularities of ordinary deformation rings
On modular representations of $\text{Gal}(\overline{\mathbb Q}/\mathbb Q)$ arising from modular forms
Lifting Galois representations
$p$-divisible groups, finite groups and filtered modules
An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the $\operatorname{mod} p$ cohomology of $\text{GL}(n,\mathbb{Z})$
Base change and a problem of Serre
On icosahedral Artin representations
On the modularity of certain 2-adic Galois representations
Galois representations with conjectural connections to arithmetic cohomology
Deforming Galois representations and the conjectures of Serre and Fontaine-Mazur.
Galois representations.
$p$-adic Hecke algebras for $GL(2)$
On Rumely's local-global principle
Modular elliptic curves and Fermat's Last Theorem
Ring-theoretic properties of certain Hecke algebras
On deformation rings and Hecke rings
Ramified deformation problems
On the modularity of 2-adic potentially semi-stable deformation rings
Symmetric power functoriality for holomorphic modular forms
Symmetric power functoriality for holomorphic modular forms. II.
Abelian surfaces over totally real fields are potentially modular
Minimal modularity lifting for nonregular symplectic representations
Strata Hasse invariants, Hecke algebras and Galois representations
$p$-adic Hilbert modular forms of weight 1
The fundamental lemma for unitary groups
On Serre's reciprocity conjecture for 2-dimensional mod $p$ representations of $\text{Gal}(\overline{\mathbb Q}/\mathbb Q)$
Modularity lifting theorems for ordinary Galois representations
Potential automorphy and change of weight
On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms
A gluing lemma and overconvergent modular forms
Automorphic forms and rational homology 3-spheres
The $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$
Elliptic curves over real quadratic fields are modular
On a conjecture of Conrad, Diamond, and Taylor
On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
On the density of modular points in universal deformation spaces
The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151)
The conjectural connections between automorphic representations and Galois representations
On the image of complex conjugation in certain Galois representations
Level-raising and symmetric power functoriality, I
Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case
Even Galois representations and the Fontaine–Mazur conjecture. II
Potential modularity – a survey
Completed cohomology – a survey
Modularity of nearly ordinary 2-adic residually dihedral Galois representations
The Fontaine-Mazur conjecture for $ {GL}_2$
On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne
Homological Dimension in Local Rings
Compatibility of local and global Langlands correspondences
Groupes de Picard et problèmes de Skolem. II
Potential Automorphy of Odd-Dimensional Symmetric Powers of Elliptic Curves and Applications
Construction de représentations $p$-adiques
Artin’s conjecture for representations of octahedral type
On Euler Products and the Classification of Automorphic Forms II
Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
Formes modulaires de poids $1$
Modularity of certain potentially Barsotti-Tate Galois representations
On degree 2 Galois representations over 𝔽 ₄
Ordinary representations and modular forms
REMARKS ON A CONJECTURE OF FONTAINE AND MAZUR
SUR QUELQUES REPRÉSENTATIONS MODULAIRES ET $p$-ADIQUES DE $\mathrm{GL}_2(\bm{Q}_{p})$. II
Modularity of some potentially Barsotti–Tate Galois representations
Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
Galois representations and modular forms
Modularity lifting in parallel weight one
Automorphy and irreducibility of some l-adic representations
Automorphy lifting for residually reducible 𝑙-adic Galois representations
Nearly ordinary Galois deformations over arbitrary number fields
Proof of de Smit’s conjecture: a freeness criterion
Möbius orthogonality for generalized Morse-Kakutani flows
A torsion Jacquet-Langlands correspondence
The Sato-Tate conjecture for Hilbert modular forms
Potentially semi-stable deformation rings
Classical and overconvergent modular forms
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