Timeline for Elliptic-curve related equivalence between fields of different characteristic?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16, 2016 at 0:24 | vote | accept | Andrew Poelstra | ||
| Sep 15, 2016 at 23:08 | comment | added | Felipe Voloch | @JeremyRouse I was just thinking along the same lines and I think that does it. | |
| Sep 15, 2016 at 23:07 | comment | added | Jeremy Rouse | Here's an idea. The trace of Frobenius on a $j=0$ elliptic curve (for $p \equiv 1 \pmod{3}$) is given by the representation of $p$ by the form $x^{2} + xy + y^{2}$, which is related to the representation of $4p$ in the form $x^{2} + 3y^{2}$. Since $(p+1-q)^2 + 3u^{2} = 4p$, then $(q+1-p)^{2} + 3u^{2} = 4q$. | |
| Sep 15, 2016 at 23:07 | comment | added | Felipe Voloch | @QiaochuYuan In the prime field case every value in the Hasse interval corresponds to a curve, by a result of Deuring. | |
| Sep 15, 2016 at 23:03 | comment | added | Qiaochu Yuan | Surely being in the Hasse interval is necessary but not sufficient, right? | |
| Sep 15, 2016 at 22:47 | history | edited | Felipe Voloch | CC BY-SA 3.0 |
added 125 characters in body
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| Sep 15, 2016 at 22:30 | history | answered | Felipe Voloch | CC BY-SA 3.0 |