most recent 30 from http://mathoverflow.net 2013-05-26T02:42:44Z http://mathoverflow.net/feeds/question/49015 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/49015/did-grothendieck-write-about-modular-forms James D. Taylor 2010-12-11T04:16:49Z 2010-12-11T21:38:32Z

<p>This question might be astoundingly naive, because my understanding of modular forms is so meek. It occurred to me that the reason I was never able to penetrate into the field of modular forms, automorphic forms, the Langland's program and so forth was because my appeal is to things that have the feel of SGA1, and those things do not.</p> <p>I was wondering, therefore, if Grothendieck had devoted thought to this, and if so where it can be found, and how it is treated in the field at the moment.</p>

http://mathoverflow.net/questions/49015/did-grothendieck-write-about-modular-forms/49023#49023 Joël 2010-12-11T06:17:31Z 2010-12-11T06:17:31Z

<p>No.</p> <p>That is perhaps a little too categorical, but a mathscinet search with Grothendieck as author and "modular form" or "forme modulaire" as "anywhere" gives no result. I don't remember him mentionning modular forms in "Recoltes et Semailles" either.</p> <p>More to the point, it is a commonplace in the field of modular and automorphic forms to wish that Grothendieck had given some time to the subject -- and made it a little more "Grothendieck-style". Pierre Cartier gave a talk at the IHES in January 2009 where he deplored that "Grothendieck and Langlands never met".</p> <p>Also, the correspondence between Serre and Grothendieck contains several letters where Serre tries to attract Grothendieck to the subject of modular forms, and where Grothendieck doesn't conceal his disinterest (to say the least).</p>

http://mathoverflow.net/questions/49015/did-grothendieck-write-about-modular-forms/49081#49081 François Brunault 2010-12-11T21:38:32Z 2010-12-11T21:38:32Z

<p>I don't know any published work by Grothendieck specifically on modular forms.</p> <p>It seems however that Grothendieck has spent some time thinking about moduli spaces of elliptic curves, for example. He has written a very long manuscript "La longue marche à travers la théorie de Galois", which is about what is now called Teichmüller theory, if I'm not mistaken. At some point, he even seems to do some "explicit" computations... I don't know this text very well though, so I would appreciate the opinion of other people about it (note that the text isn't available anymore on the Grothendieck Circle website).</p> <p>I would also say that there are at present many approaches of modular forms in the "Grothendieck style". Here I would mention the whole theory of automorphic forms, by Deligne, Langlands and many others, which is at the same time very abstract and very powerful.</p>