Timeline for Symmetric power lift of modular forms
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8 at 22:40 | comment | added | user523984 | @Olivier you are conflating a subtle problem (whether the image is open in the $\mathbf{Z}_p$ points of some algebraic group) with an easy one. The image of $(k-1)$th powers (for $k \ge 2$) is an infinite set inside the one-dimensional variety $\mathbf{G}_m$ as so is certainly Zariski dense. | |
| Nov 7 at 20:40 | comment | added | Olivier | This can't be true, as the determinant of the image contains only $k-1 $-th powers (there are other much more subtle obstructions). | |
| Mar 25 at 18:44 | comment | added | user15243 | Can we say that if $f$ is a non-CM form, then the Zariski closure of the Galois representation contains ${\mathrm{GL}}_2$? | |
| Mar 20 at 15:09 | history | bounty ended | CommunityBot | ||
| Mar 15 at 18:41 | comment | added | user15243 | claymath.org/library/proceedings/cmip013c.pdf Here, in page no 483, the author showed that two cusp forms can give same symmetric cube without being a twist of each other. So I'm not able to understand what you wrote in the second paragraph of your answer. | |
| Mar 14 at 20:38 | comment | added | user15243 | Thanks for the answer. I tried to understand it but could not figure it out. Can you provide some references? | |
| Mar 12 at 20:44 | history | answered | user523984 | CC BY-SA 4.0 |