On ordinary ?-adic representations associated to modular forms

1988/10/01 by Andrew Wiles, A. Wiles · 338 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Mathematics #Modular design #Pure mathematics #advanced mathematical theories

paper · doi:10.1007/bf01394275

published in Inventiones mathematicae 94(3), 529-573 (Springer Science+Business Media)

openalex publication_date 1988/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Citations

• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II

Cited by

• Elliptic curves over real quadratic fields are modular
• Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms
• Pseudo-repr�sentations
• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• On anticyclotomic Euler and Kolyvagin systems
• Canonical periods and congruence formulae
• Galois representations associated to Siegel modular forms of low weight
• Stable free lattices in residually reducible Galois deformations and control theorem of Selmer groups
• Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case
• On certain constructions of p-adic families of Siegel modular forms of even genus
• Pseudorepresentations not arising from genuine representations
• On the computation of base-change lifts and lifts of Hida families
• p-adic heights of generalized Heegner cycles
• Big principal series, p-adic families and L-invariants
• Comparison of canonical periods under base change
• Hirzebruch-Zagier classes and rational elliptic curves over quintic fields
• From potential modularity to modularity for integral Galois representations and rigid Calabi-Yau threefolds
• On the symmetric powers of cusp forms on GL (2) of icosahedral type
• Conductors in p-adic families
• On the Iwasawa main conjectures for modular forms at non-ordinary primes
• Ramification of Hilbert eigenvarieties at classical points
• On the non-vanishing of generalized Kato classes for elliptic curves of rank 2
• Stable \mathbbI-free lattices and the two-variable algebraic p-adic L-functions in residually reducible Hida deformation
• Représentations galoisiennes automorphes et conséquences arithmétiques des conjectures de Langlands et Arthur
• A semi-ordinary p-stabilization of Siegel Eisenstein series for symplectic groups and its p-adic interpolation
• On certain cohomology groups attached to \mathfrakp^∞-towers of quaternionic Hilbert modular varieties
• T-ideals of Cayley Hamilton algebras
• The completed Kirillov model and local-global compatibility for functions on Igusa varieties
• Arithmetic Satake compactifications and algebraic Drinfeld modular forms
• On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights
• Noncommutative Iwasawa theory arising from Hecke algebras
• Elliptic Curves over Real Quadratic Fields are Modular
• Galois representations modulo p and cohomology of Hilbert modular varieties
• The Iwasawa Main Conjectures for \rm GL₂ and derivatives of p-adic L-functions
• On the norms of p-stabilized elliptic newforms (with an appendix by Keith Conrad)
• On two dimensional weight two odd representations of totally real fields
• On the Gross-Stark Conjecture
• Companion forms over totally real fields
• Sur les représentations p-adiques géométriques de conducteur 1 et de dimension 2 de G_\Q
• Congruences of algebraic L-functions of motives
• Recipes to Fermat-type equations of the form x^r + y^r = Cz^p
• On the congruence ideal associated to p-adic families of Yoshida lifts
• Strong local-global phenomena for Galois and automorphic representations
• Level raising for p-adic Hilbert modular forms
• The Geometry of Hida Families and Λ-adic Hodge Theory
• Ring-Theoretic Properties of Certain Hecke Algebras
• The Iwasawa Conjecture for Totally Real Fields
• The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in the Hecke algebra
• Ramification of the Eigencurve at Classical RM Points
• A remark on non-integral p-adic slopes for modular forms