Timeline for Which Shimura varieties are known to be automorphic?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 18, 2011 at 21:46 | vote | accept | B R | ||
| Sep 17, 2011 at 18:57 | comment | added | B R | Thanks for the links, they did give me some ideas for searching the literature. | |
| Sep 17, 2011 at 16:57 | answer | added | Alex | timeline score: 14 | |
| Sep 17, 2011 at 10:47 | comment | added | Kevin Buzzard | I think the fundamental lemma comes for free nowadays. As for the current state of stabilizing the trace formula I'd be tempted to look at Harris' book project: fa.institut.math.jussieu.fr/node/29 . I'm sorry I can't just tell you the answer -- I am no expert. | |
| Sep 16, 2011 at 20:44 | comment | added | B R | Kevin, that would be nice! I don't quite see it (though as an outsider, I may miss certain implications). Milne says that to show that the zeta function of a Shimura variety is automorphic, you need 1) a description of the points of the variety over a finite field 2) "a combinatorial argument" using the trace formula and the fundamental lemma. Milne's paper (and his references) just deals with 1). I don't think 2) comes for free (right?). But it is nice to see that there are some somewhat general results known for groups of type A and C. | |
| Sep 16, 2011 at 19:50 | comment | added | Kevin Buzzard | This question is perhaps answered in the first few paragraphs of the following paper of Milne on the subject: jmilne.org/math/articles/2008b.pdf | |
| Sep 16, 2011 at 19:12 | history | asked | B R | CC BY-SA 3.0 |