Modularity lifting in parallel weight one

Abstract

We prove an analogue of the main result of Buzzard and Taylor [Buzzard, K.; Taylor, R.: Companion forms and weight one forms. Ann. of Math. (2) 149 (1999), no. 3, 905–919. MR1709306 (2000j:11062)] for totally real fields in which $p$ is unramified. This can be used to prove certain cases of the strong Artin conjecture over totally real fields.<br/>