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Geometric level raising for p-adic automorphic forms
| Content Provider | Scilit |
|---|---|
| Author | Newton, James John Michael |
| Copyright Year | 2010 |
| Description | Journal: Compositio Mathematica 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. We show that certain families of forms old at a prime l intersect with families of l-new forms (at a non-classical point). 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. |
| Ending Page | 354 |
| Starting Page | 335 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x10004999 |
| Journal | Compositio Mathematica |
| Issue Number | 2 |
| Volume Number | 147 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2010-08-05 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Adic Automorphic Forms |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
