Level raising and completed cohomology

Details Level raising and completed cohomology Level raising and completed cohomology

2010-08-09

arxiv.org/abs/1008.1487v2

International Mathematics Research Notices 2011(11):2565-2576

Mathematics

Number Theory

7 pages. Some small changes and reference updates

Scientific paper

10.1093/imrn/rnq171

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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