Timeline for BSD for modular forms
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2011 at 19:30 | answer | added | William Stein | timeline score: 3 | |
| Nov 15, 2010 at 4:06 | vote | accept | schur | ||
| Oct 19, 2010 at 8:51 | answer | added | Olivier | timeline score: 8 | |
| Oct 19, 2010 at 8:14 | comment | added | Olivier | Dear Alex, your question wasn't more elementary, because you asked for some interpretation of the Tamagawa number conjecture in terms of natural objects. To find this might be a difficult task (especially since natural can be in the eye of the beholder). However, specializing Tamagawa Number Conjectures to the case of modular forms is an interesting exercise, not at all easy by the way, but certainly doable (and done 15 years ago). One last thing to Ian: the references I mentioned should also do for twists by characters but you should know that for some twists, things get much harder. | |
| Oct 19, 2010 at 8:09 | comment | added | Olivier | Dear Ian, In the case of a normalized eigenform over $\mathbb Q$ (which I gather is your case of interest), then everything can be done explicitly, and in fact has been. Two good references are K.Kato Iwasawa theory and p-adic Hodge theory (Kodaira math. 1993) and $p$-adic Hodge theory and values of zeta functions of modular forms (Asterisque 2004). That said, there is another place where everything is checked quite explicitly, and this is the PhD. thesis of M.Gealy. The first and third references are online (I think) ut if you have trouble finding them, you could always e-mail me. | |
| Oct 19, 2010 at 6:53 | answer | added | David Loeffler | timeline score: 4 | |
| Oct 19, 2010 at 1:45 | comment | added | Alex B. | In the case of modular forms, the circle of conjectures is called "Bloch-Kato conjecture" rather than BSD. More precisely, you want to explicate the Bloch-Kato conjecture for the motif attached to your modular (new)form. Not sure if this has been done explicitly for modular forms (even my more elementary question about Artin L-functions is still unanswered), but if you are familiar with the Bloch-Kato formalism, then that's the place to look. | |
| Oct 19, 2010 at 0:47 | history | asked | schur | CC BY-SA 2.5 |