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

Payman L Kassaei, Shu Sasaki, Yichao Tian

Number 17
Author Shu Sasaki
Year 2013

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.

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