Timeline for Finite quotients of the absolute Galois group of $\mathbb{Q}$ via torsion of elliptic curves
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 25, 2021 at 21:50 | answer | added | Will Sawin | timeline score: 4 | |
| Apr 25, 2021 at 18:21 | comment | added | Arno Fehm | Even something stronger holds: The field obtained by adjoing all $E[p]$ to $\mathbb{Q}$, for all ellliptic curves $E$ and all $p$, is still very far away from the algebraic closure $\overline{\mathbb{Q}}$ (in fact it is a Hilbertian field). I know of no similar result when running over all abelian varieties though. | |
| Apr 25, 2021 at 16:44 | comment | added | Chris Wuthrich | If your finite group has a 2-dimensional representation, then en.wikipedia.org/wiki/Serre%27s_modularity_conjecture implies that it comes from a modular form if it is odd etc. But only few of those come from elliptic curves. | |
| Apr 25, 2021 at 16:10 | comment | added | Wojowu | Every such action is odd, meaning the complex conjugation is mapped to multiplication by $-1$ (this is certainly true for elliptic curves and I believe also for abelian varieties). So any quotient which identifies complex conjugation and identity won't arise this way. | |
| Apr 25, 2021 at 16:03 | review | First posts | |||
| Apr 25, 2021 at 17:27 | |||||
| Apr 25, 2021 at 15:56 | history | asked | Leray J | CC BY-SA 4.0 |