Timeline for Newton polygons of modular polynomials
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Aug 1, 2014 at 14:04 | history | bounty ended | Lev Borisov | ||
| S Aug 1, 2014 at 14:04 | history | notice removed | Lev Borisov | ||
| Jul 31, 2014 at 17:33 | comment | added | Lev Borisov | @WillSawin Great, I can definitely follow it now. Yes, I think this calculation would indicate that the restriction of this line bundle to $X_0(n)$ would only be the sum of the divisors obtained from traces of Heegner points, so it would not be any "new" bundle. | |
| Jul 31, 2014 at 17:06 | comment | added | Will Sawin | I worked out in more detail my thoughts about the bottom corner. I think this is more related to Heegner points of conductor $1$, because these are the CM points associated to split ideals in $\mathbb Z[\omega]$, not in a subring. | |
| Jul 29, 2014 at 23:42 | comment | added | Lev Borisov | Will, I was happy with your answer, thank you! I didn't quite follow the arguments regarding the bottom corner, but, certainly, if your Heegner point guess is true, then it would dash my faint hope of getting some more sporadic divisors from this construction. I assume that these would be Heegner points for the conductor not coprime (equal?) to the level, which are generally avoided in applications like Gross-Zagier formula. Am I correct? | |
| Jul 29, 2014 at 15:13 | comment | added | Will Sawin | is there any more information you would like in my answer? | |
| Jul 26, 2014 at 16:12 | vote | accept | Lev Borisov | ||
| Jul 26, 2014 at 15:29 | answer | added | Will Sawin | timeline score: 6 | |
| Jul 26, 2014 at 12:18 | comment | added | Lev Borisov | Just to make this a bit more interesting: one can associate to every side of the Newton polygon a line bundle on the modular curve. It is interesting to see in examples whether (after subtracting a multiple of the divisor of modular forms) the resulting point on the Jacobian is torsion. | |
| S Jul 26, 2014 at 11:13 | history | bounty started | Lev Borisov | ||
| S Jul 26, 2014 at 11:13 | history | notice added | Lev Borisov | Draw attention | |
| Jul 23, 2014 at 21:07 | history | asked | Lev Borisov | CC BY-SA 3.0 |