Timeline for Order of torsion group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 30, 2015 at 18:46 | comment | added | Bobby Grizzard | @Suman First of all, I assume since you accepted this answer that you meant in your original question that the elliptic curves should be defined over $\mathbb{Q}$, and you want to know about $E(K)_tors$ for such curves, where $K$ is the compositum of all quadratic fields. The fact that the curves are defined over $\mathbb{Q}$ is of course crucial in the Fujita & Laska-Lorenz results mentioned above. Secondly, I have an easy way to see that the order of the group is finite. It's maybe too long for a comment here, so see my "answer" below. | |
| Oct 6, 2013 at 3:23 | vote | accept | Suman | ||
| May 1, 2013 at 7:24 | comment | added | Chema Tornero | The first proof I know of this fact goes back to Laska & Lorenz (J. Reine Angew. Math. 355 (1985) 163-172). They proved that there were at most 31 possible torsion subgroups, and then Fujita showed that there were in fact only 20. Unfortunately, I don't have the paper around right now and I can't recall if their proof of finiteness is easy or not (in fact they might even refer to a previous paper, you know how this goes...). | |
| Apr 29, 2013 at 10:25 | comment | added | Suman | Is there an easier method to prove that order of the group will be finite ?? | |
| Apr 29, 2013 at 10:11 | vote | accept | Suman | ||
| Oct 6, 2013 at 3:23 | |||||
| Apr 29, 2013 at 10:00 | history | answered | Chema Tornero | CC BY-SA 3.0 |