Timeline for Degree of morphisms and isogenies
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2020 at 17:54 | vote | accept | Watson | ||
| Apr 15, 2020 at 9:47 | history | edited | Ben Smith | CC BY-SA 4.0 |
Fixed mistakes in definition of $\psi$ and $\phi$.
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| Apr 15, 2020 at 9:42 | comment | added | Ben Smith | @Watson you're right, I compounded a few typos in my working. I think you might have an $i$ too many on the $y$-coordinate of $\phi$, too. Will update my answer accordingly. | |
| Apr 14, 2020 at 18:38 | comment | added | Watson | I think that taking $\dfrac{X + i}{X - i}$ in the first coordinate of $\psi$, and by taking $$\phi(u,v) = \left( -i \cdot\frac{u + i}{u - i}, i \cdot\frac{(i-1)v}{(u-i)^2} \right),$$ does give a morphism $f_1$ which is defined over $\Bbb F_p$. | |
| Apr 14, 2020 at 15:17 | comment | added | Watson | Dear Ben Smith, thank you so much for your helpful answer. But why is $f_1$ defined over $\Bbb F_p$ ? According to my computation, the second component is not invariant under swapping $i$ and $-i$ (set e.g. $X=0, Y=1, p=7$, so $d=2$). | |
| Apr 14, 2020 at 13:15 | review | First posts | |||
| Apr 14, 2020 at 13:32 | |||||
| Apr 14, 2020 at 13:11 | history | answered | Ben Smith | CC BY-SA 4.0 |