Talk:Modular curve

To do:

most importantly, a picture of modular figure (for the modular group itself);
algebraic definition of modular curves (Nick Katz's approach);
towers of modular curves, adelic interpretation, Hecke correspondences;
examples of modular curves mod p, short description of Eichler-Shimura;
other applications, e.g. Drinfeld-Vladuts, Ramanujan graphs.

Feel free to contribute to any of these! Arcfrk 02:15, 5 April 2007 (UTC)[reply]

Better to put the group (Gamma) on the left, thus Gamma\H in place of H\Gamma etc. globally.

[John McKay]24.200.80.81 09:38, 10 September 2007 (UTC)[reply]

Monstrous moonshine

I feel that this section is out of place here, even aside from its inferior quality. It should be enough just to mention that modular curves of genus 0 are connected with the Monster finite simple group and refer to the reasonably well-written article on the moonshine conjectures for details. Arcfrk (talk) 17:09, 13 December 2009 (UTC)[reply]

I don't see a serious problem: the order of material should probably be switched around, though. Hauptmodul, as the German terminology suggests, goes back to the Klein-Fricke era, and is quite classical therefore. Perhaps some comments first on how the genus of a modular curve is calculated, and then the genus 0 case (happens only finitely often); and then some mention of the interest from the finite group side. Charles Matthews (talk) 19:11, 13 December 2009 (UTC)[reply]