English

Level raising and completed cohomology

Number Theory 2011-07-06 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1008.1487,
  title  = {Level raising and completed cohomology},
  author = {James Newton},
  journal= {arXiv preprint arXiv:1008.1487},
  year   = {2011}
}

Comments

7 pages. Some small changes and reference updates

R2 v1 2026-06-21T15:58:33.166Z