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Saito-Kurokawa lifts and applications to the Bloch-Kato conjecture
| Content Provider | Semantic Scholar |
|---|---|
| Author | Brown, Jim |
| Copyright Year | 2005 |
| Abstract | Let f be a newform of weight 2k−2 and level 1. In this paper we provide evidence for the Bloch-Kato conjecture for modular forms. We demonstrate an implication that under suitable hypotheses if | Lalg(k, f) then p | #Hf (Q,Wf (1− k)) where p is a suitably chosen prime and a uniformizer of a finite extension K/Qp. We demonstrate this by establishing a congruence between the Saito-Kurokawa lift Ff of f and a cuspidal Siegel eigenform G that is not a Saito-Kurokawa lift. We then examine what this congruence says in terms of Galois representations to produce a non-trivial p-torsion element in Hf (Q,Wf (1− k)). |
| Starting Page | 290 |
| Ending Page | 322 |
| Page Count | 33 |
| File Format | PDF HTM / HTML |
| DOI | 10.1112/S0010437X06002466 |
| Volume Number | 143 |
| Alternate Webpage(s) | http://www.math.clemson.edu/~jimlb/ResearchPapers/CompMath143(2)2007.pdf |
| Alternate Webpage(s) | http://www.math.clemson.edu/~jimlb/ResearchPapers/level1paper2005.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0512279v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0512279v1.pdf |
| Alternate Webpage(s) | http://www.math.caltech.edu/~jimlb/level1paper2005.pdf |
| Alternate Webpage(s) | https://doi.org/10.1112/S0010437X06002466 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
