Level Raising and Completed Cohomology

We describe an application of Poincaré duality for completed homology spaces (as defined by Emerton) to level raising for p-adic modular forms. This allows us to give a new description of the image of Chenevier’s p-adic Jacquet–Langlands map between an eigencurve for a definite quaternion algebra and an eigencurve for GL
2
. The points on the eigencurve at which we “raise the level” are (nonsmooth) points of intersection between an “old” and a “new” component.