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arXiv · 1008.1487

Level raising and completed cohomology

James Newton
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Abstract

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 (non-smooth) points of intersection between an "old" and a "new" component.

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James Newton. 2011-07-05. Level raising and completed cohomology. https://doi.org/10.1093/imrn%2Frnq171

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