Timeline for Examples of the moduli space of X giving facts about a certain X
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2022 at 6:37 | answer | added | Jonny Evans | timeline score: 3 | |
| Oct 22, 2022 at 12:28 | answer | added | LeechLattice | timeline score: 2 | |
| Nov 25, 2016 at 23:08 | answer | added | Sean Rostami | timeline score: 3 | |
| Oct 18, 2010 at 3:37 | vote | accept | Brendan Fong | ||
| May 28, 2010 at 17:37 | answer | added | Csar Lozano Huerta | timeline score: 5 | |
| May 28, 2010 at 10:19 | comment | added | Minhyong Kim | It's fun, however, to speculate that the above two are examples. | |
| May 28, 2010 at 10:02 | comment | added | Minhyong Kim | It's also amusing to note that the proof of the Mordell conjecture (using $M_g$) or the modularity conjecture for elliptic curves (using modular curves) are not examples of the sort we want, strictly speaking. | |
| May 28, 2010 at 9:52 | comment | added | Minhyong Kim | Similar in nature to Brian's example, there is the arithmetic moduli of principally polarized abelian varieties (and compactifications). Analyzing the height function on this space was essential to the deep results concerning Galois actions on the Tate module of an abelian variety, such as its semi-simplicity or the Tate conjecture. I was going to mention the Shafarevich conjecture as well (inextricably tied to the other statements), but that's not about a single abelian variety. | |
| May 28, 2010 at 7:31 | answer | added | John Doe | timeline score: 3 | |
| May 28, 2010 at 1:11 | comment | added | BCnrd | Mazur's deep study of modular curves over $\mathbf{Q}$, especially understanding the arithmetic of their Jacobians (something impossible to express without the moduli space itself), was the key to his determination of the possibilities for torsion groups in Mordell-Weil groups of elliptic curves over $\mathbf{Q}$. Refinement of these ideas was used by Merel for number fields. | |
| May 27, 2010 at 22:59 | answer | added | Lars | timeline score: 1 | |
| May 27, 2010 at 22:01 | answer | added | Dmitri Panov | timeline score: 3 | |
| May 27, 2010 at 8:33 | answer | added | Andrea Ferretti | timeline score: 25 | |
| May 27, 2010 at 7:54 | answer | added | Charles Matthews | timeline score: 3 | |
| May 27, 2010 at 6:58 | history | asked | Brendan Fong | CC BY-SA 2.5 |