Timeline for A $\mathbb{Q}$-rational canonical model for $X(N)$?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 23, 2013 at 14:18 | comment | added | user29283 | This $Y(N)$ represents the moduli problem of pairs $(E,i)$ consisting of elliptic curves $E \rightarrow S$ (with $S$ a $\mathbf{Z}[1/N]$-scheme) and $i:(\mathbf{Z}/N\mathbf{Z})_S \times \mu_N \simeq E[N]$ is an isomorphism of $S$-group schemes. It is a smooth affine curve over $\mathbf{Z}[1/N]$ with geometrically connected fibers. The "classical" moduli problem uses an isomorphism between $E[N]$ and the constant $S$-group scheme $(\mathbf{Z}/N\mathbf{Z})_S^2$, so the relative Weil pairing of the standard basis specifies a map from $S$ to ${\rm{Spec}}(\mathbf{Z}[1/N][X]/(\Phi_N))$. | |
| Apr 23, 2013 at 12:55 | answer | added | François Brunault | timeline score: 1 | |
| Apr 23, 2013 at 9:12 | history | asked | Will Chen | CC BY-SA 3.0 |