Geodesic
Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case
Forum of Mathematics, Sigma, Tome 2 (2014)

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We extend the modularity lifting result of P. Kassaei (‘Modularity lifting in parallel weight one’,J. Amer. Math. Soc.26 (1) (2013), 199–225) to allow Galois representations with some ramification at $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$ . We also prove modularity mod 5 of certain Galois representations. We use these results to prove 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 P. Kassaei (‘Modularity lifting in parallel weight one’, J. Amer. Math. Soc.26 (1) (2013), 199–225). 
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     author = {PAYMAN L. KASSAEI and SHU SASAKI and YICHAO TIAN},
     title = {Modularity lifting results in parallel weight one and applications to the {Artin} conjecture: the tamely ramified case},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
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PAYMAN L. KASSAEI; SHU SASAKI; YICHAO TIAN. Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case. Forum of Mathematics, Sigma, Tome 2 (2014). doi: 10.1017/fms.2014.12

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