Timeline for Books you would like to read (if somebody would just write them…)
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 27, 2011 at 5:16 | comment | added | David Hansen | Dear Emerton: Then I will do that. Many thanks for your insight and perspective! | |
| Jan 27, 2011 at 4:42 | comment | added | Emerton | ... go further with the theory; they are not really simplifications (as opposed to modifications) of the argument (in my view). If one is at the point of wanting to understand Hecke algebras in a hands-on way via Jacquet--Langlands (although I'm not sure exactly what you mean by this; I've always found Hecke algebras on spaces of modular forms to be pretty hands-on things), then you have gone beyond an amateur interest, and should just learn the subject the way you learn any other subject, beginning with the available existing text-book sources and then moving onto the research literature. | |
| Jan 27, 2011 at 4:39 | comment | added | Emerton | ... the same tight control of the geometry as one has in the context of modular curves, but it's a matter of one's predilections as to whether it counts as a simplification. (This comment just reflects my own training, which finds Ribet's arithmetic geometry arguments quite a bit easier to follow than the proof of base change.) I think that, with the sole exception of Diamond's paper, which really does count as an unambiguous simplification, these other approaches to the argument just reflect modifications of technique in order to ... | |
| Jan 27, 2011 at 4:33 | comment | added | Emerton | Dear David, Yes, but these improvements are amply documented in the research literature; I don't see the need for another text at the moment, given the existence of Cornell, Silverman, and Stevens. After all, the paper of Diamond in Inventiones is well-written, so if one understands everything in Cornell, Silverman, and Stevens except the mult. one statements, it is no trouble to modify things so as to incorporate the results of Diamond's article. As for replacing the geometric arguments for level lowering by base change, this is very powerful in those contexts where one doesn't have ... | |
| Jan 25, 2011 at 16:53 | comment | added | David Hansen | Emerton, I have this book but unfortunately haven't had the time to dive into it yet. My impression (horribly mistaken?) was that the last fifteen years have seen some simplifications and improvements to the proof - e.g. appeal to base change to avoid level lowering, appeal to Jacquet-Langlands to study the Hecke algebras in a more hands-on way, the Diamond-Fujiwara version of patching and concomitant avoidance of appeal to multiplicity one, etc. | |
| Jan 24, 2011 at 14:16 | comment | added | Chandan Singh Dalawat | There are also the DDT notes, now available on Darmon's website, along with other related material. | |
| Jan 24, 2011 at 12:46 | comment | added | Emerton | Dear David, This exists in textbook form: as I noted in another comment, there is the book Modular forms and Fermat's Last Theorem (Cornell, Silverman, Stevens eds.). | |
| Jan 24, 2011 at 12:17 | history | answered | David Hansen | CC BY-SA 2.5 |