Timeline for Why all supersingular elliptic curves over $\bar{\mathbb{F}_p}$ are isogenous?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 16, 2023 at 12:50 | vote | accept | HaomengXu | ||
| S Apr 16, 2023 at 12:21 | vote | accept | HaomengXu | ||
| S Apr 16, 2023 at 12:50 | |||||
| Apr 16, 2023 at 12:21 | vote | accept | HaomengXu | ||
| S Apr 16, 2023 at 12:21 | |||||
| Apr 16, 2023 at 8:14 | answer | added | djao | timeline score: 3 | |
| Apr 16, 2023 at 8:07 | answer | added | Watson | timeline score: 4 | |
| Apr 15, 2023 at 22:12 | comment | added | Raju | You can also see Theorem 9.6 of <arxiv.org/pdf/1704.00335.pdf> (and the description of this result on p. 2). This in fact shows that for any fixed $\ell\neq p$, any pair of supersingular elliptic curves over $\bar{\mathbb{F}}_p$ are $\ell$-primarily isogenous. | |
| Apr 15, 2023 at 22:11 | comment | added | Viktor Vaughn | Crossposted to MSE | |
| Apr 15, 2023 at 16:36 | comment | added | Jason Starr | I think that probably goes back to Deuring, but it certainly follows from Tate's theorem about isogeny classes and Tate modules. Since all supersingular elliptic curves have endomorphism algebras equal to maximal orders in the unique quaternion algebra ramified only at $p$ (and $\infty$), the associated rings $\mathbb{Z}_\ell\otimes \text{End}$ are isomorphic. Now you can apply Tate's theorem. | |
| Apr 15, 2023 at 14:11 | history | edited | HaomengXu | CC BY-SA 4.0 |
added 605 characters in body
|
| Apr 15, 2023 at 13:41 | history | edited | HaomengXu | CC BY-SA 4.0 |
added 68 characters in body
|
| S Apr 15, 2023 at 13:22 | review | First questions | |||
| Apr 15, 2023 at 15:43 | |||||
| S Apr 15, 2023 at 13:22 | history | asked | HaomengXu | CC BY-SA 4.0 |