Timeline for Prove that $\Bbb C[x,y]/(x^3+y^3-1)$ is not a UFD
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2023 at 3:28 | comment | added | GH from MO | Very nice argument. It also follows along these lines that $R^\times$ is generated by $\mathbb{C}^\times$ and the exhibited units $\eta_j$. Indeed, the divisors $\mathrm{div}(\eta_j)$ generate an index $3$ subgroup in the group of degree zero divisors supported on $\{P,Q,R\}$, with cosets being represented by the divisors $0$, $Q-R$, $R-Q$. However, $Q\not\sim R$, whence the subgroup in question is the group of all principal divisors supported on $\{P,Q,R\}$. This also shows that $\mathrm{Pic}(\tilde E,S)$ in my post is isomorphic to $\mathbb{Z}\times(\mathbb{Z}/3)$. | |
| S Nov 10, 2023 at 19:05 | review | First answers | |||
| Nov 10, 2023 at 19:18 | |||||
| S Nov 10, 2023 at 19:05 | history | answered | user516477 | CC BY-SA 4.0 |