Geometric level raising for p-adic automorphic forms

We present a level raising result for families of p-adic automorphic forms for a definite quaternion algebra D over Q. The main theorem is an analogue of a theorem for classical automorphic forms due to Diamond and Taylor. One of the ingredients in the proof of Diamond and Taylor’s theorem (which also played a role in earlier work of Taylor) is the definition of a suitable pairing on the space of automorphic forms. In our situation one cannot define such a pairing on the infinite dimensional space of p-adic automorphic forms, so instead we introduce a space defined with respect to a dual coefficient system and work with a pairing between the usual forms and the dual space. A key ingredient is an analogue of Ihara’s lemma which shows an interesting asymmetry between the usual and the dual spaces. Our research grew out of a conjecture of Paulin, predicting a level raising phenomenon on the GL2eigencurve. Our results prove certain cases of this conjecture, by way of the p-adic Jacquet-Langlands map constructed by Chenevier. A further application is a description of an eigenvariety of automorphic forms for D that are new at a prime l.