Timeline for The ideal in $\mathbb{Z}[x]$ of all vanishing polynomials of a curve automorphism
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2023 at 19:44 | comment | added | Dimitri Koshelev | I appreciate very much your comments. But to be honest, it becomes difficult for me to track all your thoughts. Could you advise sources in which similar questions are touched upon? I need to obtain more experience on this topic to continue the discussion. | |
| Oct 30, 2023 at 19:25 | comment | added | Will Sawin | @DimitriKoshelev This happens if and only if $C/\langle \alpha \rangle $ has genus $0$ but $C$ does not have genus $0$. The quotient has genus $0$ if and only if the average of $g(i)$ for $i$ from $0$ to $n-1$ is zero. | |
| Oct 30, 2023 at 19:24 | history | edited | Will Sawin | CC BY-SA 4.0 |
added 1513 characters in body
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| Oct 30, 2023 at 19:24 | comment | added | Dimitri Koshelev | Is there at least any sufficient condition that $I_\alpha = \langle \Phi_n \rangle$ in the simplest case when $n$ is prime? In this case, the minimal polynomial is $x^n - 1$ or $\Phi_n = \sum_{i=0}^{n-1} x^i$. | |
| Oct 30, 2023 at 18:56 | comment | added | Dimitri Koshelev | I need a less expensive method (with a polylogarithmic complexity), because for huge $n$, solving a linear system is a quite slow procedure. I am right that $f$ is the product of certain cyclotomic polynomials $\Phi_{n_i}$, where $n_i \mid n$? Can we use somehow this fact to simplify search of the desired polynomial? | |
| Oct 30, 2023 at 14:37 | history | answered | Will Sawin | CC BY-SA 4.0 |