Timeline for Gouvea-Mazur conjecture
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2011 at 17:54 | comment | added | Kevin Buzzard | @Arijit: I think Wan's theorem is something like: the size of the slope $\alpha$ spaces will be the same if $k_1$ and $k_2$ are congruent mod $(p-1)p^M$ with $M=O(\alpha^2)$. It's perhaps also worth remarking that the implied constant in the $O$ depends on the level that you're working at. The classical and overconvergent conjectures are basically the same now, after Coleman's classicality result. | |
| Jul 26, 2011 at 7:37 | comment | added | David Loeffler | I don't think Coleman's work gives any explicit bounds at all. The quadratic bound you mention comes from work of Daqing Wan, "Dimension variation of classical and p-adic modular forms". I don't know of any subsequent improvements on this. | |
| Jul 26, 2011 at 1:45 | vote | accept | Arijit | ||
| Jul 26, 2011 at 1:45 | comment | added | Arijit | @ prof. Berger and Prof. Ramsey Thanks a lot for the comments. In fact I had looked at that paper by Buzzard and Calegari. I remember a result by Coleman where he shows that the Govea-Mazur conjecture is true if $k_i = O(\sqrt{m})$. Is this the best possible bound known? | |
| Jul 25, 2011 at 17:47 | answer | added | David Loeffler | timeline score: 4 | |
| Jul 25, 2011 at 16:27 | comment | added | Ramsey | By "the space of all modular forms" you probably mean the space of classical modular forms (which is actually much smaller than the space of overconvergent p-adic forms). The relation between the two is provided by Coleman's "low slope implies classical" theorems. See his papers "Classical and overconvergent modular forms" and "classical and overconvergent modular forms of higher level." | |
| Jul 25, 2011 at 16:17 | comment | added | Laurent Berger | Not an answer to your question, but you might be interested in the paper "A counterexample to the Gouvêa-Mazur conjecture", by Buzzard and Calegari. | |
| Jul 25, 2011 at 15:51 | history | asked | Arijit | CC BY-SA 3.0 |