Automorphy for some l -adic lifts of automorphic mod l Galois representations. II

2008/11/07 by Richard Taylor · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research #Galois module #Mathematics #Lemma (botany) #Pure mathematics #Mod #Dimension (graph theory) #Galois group #Automorphic form #Discrete mathematics #Algebra over a field #Agronomy

paper · doi:10.1007/s10240-008-0015-2

openalex publication_date 2008/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We extend the results of [CHT] by removing the ‘minimal ramification' condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara's lemma.

Citations

• Cohomology of Number Fields
• On Euler Products and the Classification of Automorphic Representations I
• Ring-Theoretic Properties of Certain Hecke Algebras
• On Euler Products and the Classification of Automorphic Forms II
• Modular Elliptic Curves and Fermat's Last Theorem
• Groupes réductifs sur un corps local : I. Données radicielles valuées

Cited by

• On deformation rings of residually reducible Galois representations and\n R=T theorems
• A Family of Calabi–Yau Varieties and Potential Automorphy II
• Richard Taylor (mathematician) [wikipedia]
• Sato–Tate conjecture [wikipedia]

Related

• Automorphy for some l -adic lifts of automorphic mod l Galois representations
• On the automorphy of l-adic Galois representations with small residual image
• Automorphy lifting for residually reducible l-adic Galois representations, II
• Automorphic lifts of prescribed types
• Automorphy lifting with adequate image