Talk:Modular curve
Latest comment: 14 years ago by Charles Matthews in topic Monstrous moonshine
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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)
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)
Monstrous moonshine
editI 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)
- 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)