Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case

2012/04/03 by Payman L Kassaei, Kassaei, Payman L, Shu Sasaki +3
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · doi:10.48550/arxiv.1204.0579

Abstract

We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We use these results to prove many new cases of the strong Artin conjecture over totally real fields in which 5 is unramified. As an ingredient of the proof, we provide a general result on the automatic analytic continuation of overconvergent p-adic Hilbert modular forms of finite slope which substantially generalizes a similar result in arXiv:1111.2804.

Citations

• On ordinary ?-adic representations associated to modular forms
• Caractérisation des caractères et Pseudo-caractères

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