Timeline for Criterion for generic polynomials
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2020 at 0:29 | vote | accept | Jackson Morrow | ||
| Apr 30, 2020 at 22:51 | answer | added | Jeremy Rouse | timeline score: 7 | |
| Apr 30, 2020 at 19:33 | comment | added | Jackson Morrow | @DanielLoughran Thank you for the comment! Yes I have looked at Serre's notes, and the crux of his arguement seems to be that for $x^3 + tx^2 + (t-3)x + 1$, the function $t = (x^3 - 3x + 1)/(x^2 - x)$ is $\mathbb{Z}/3\mathbb{Z}$-invariant for the action of $\mathbb{Z}/3\mathbb{Z}$ on $\mathbb{P}^1$ given by $\sigma x = 1/(1-x)$. I don't see how to adapt his arguement to my setting as the coefficients in my polynomial are non-linear. | |
| Apr 30, 2020 at 16:40 | comment | added | Daniel Loughran | If you have not done so already, I would recommend looking at Serre's "Topics in Galois Theory". In Section 1.1, he proves that the polynomial $x^3 - tx^2 + (t - 3)x + 1$ is generic for $\mathbb{Z}/3\mathbb{Z}$. Maybe his proof can be adapted to your case. | |
| Apr 30, 2020 at 15:07 | history | asked | Jackson Morrow | CC BY-SA 4.0 |