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arxiv: 1008.1487 · v2 · pith:FAVYICIOnew · submitted 2010-08-09 · 🧮 math.NT

Level raising and completed cohomology

classification 🧮 math.NT
keywords eigencurvelevelcompletedp-adicpointsraisingalgebraallows
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We describe an application of Poincar\'e 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 (non-smooth) points of intersection between an "old" and a "new" component.

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