Timeline for Example of non-modular elliptic surface?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2014 at 19:52 | comment | added | Ariyan Javanpeykar | @MohammadF.Tehrani How does the j-map lift to a self-map of $\mathbb H$? The action of PSL$_2(\mathbb Z)$ is not free, and moreover, the complex upper half-plane $\mathbb H$ is not the universal cover of the affine line PSL$_2(\mathbb Z) \backslash \mathbb H$. | |
| Oct 18, 2013 at 19:49 | comment | added | Mohammad Farajzadeh-Tehrani | We can lift the j-map to $j:\mathbb{H}\to \mathbb{H}/PSL(2,\mathbb{Z})$; since $\mathbb{H}$ is simply connected, we can then lift this to a map $j:\mathbb{H}\to\mathbb{H}$. Then for $\gamma \in G$, we have to have $j(\gamma\cdot z)=\iota(\gamma)j(z)$, for some representation $\iota:G \to PSL(2,\mathbb{Z})$ (I am assuming this lifts to $SL(2,\mathbb{Z})$ itself, which should not be a big deal for now) | |
| Oct 18, 2013 at 17:34 | comment | added | Remke Kloosterman | To be honest, I do not really understand the second part of your question. For example, why is the map H/G to H/PSL(2,Z) induced by a self map of H? You need this to have the map i:G->PSL(2,Z). | |
| Oct 17, 2013 at 23:39 | comment | added | Mohammad Farajzadeh-Tehrani | I have added a comment to the end of my question regarding your answer. What do you think of it? | |
| Oct 17, 2013 at 22:33 | history | answered | Remke Kloosterman | CC BY-SA 3.0 |