Timeline for Algebraic numbers and the complex projective line minus three points
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 22, 2013 at 9:12 | vote | accept | Colin McLarty | ||
| Jul 20, 2013 at 1:05 | answer | added | Colin McLarty | timeline score: 3 | |
| Jul 19, 2013 at 13:26 | comment | added | Jason Starr | Perhaps somebody should re-write one of these comments as an answer. | |
| Jul 19, 2013 at 5:35 | comment | added | Colin McLarty | @JSE Thanks, that's a good viewpoint to know of. | |
| Jul 19, 2013 at 5:33 | comment | added | Colin McLarty | @Felipe Voloch: I think your comments are the answer. Deligne is citing the "if and only if" statement that people often call Belyi's theorem, though in fact he is using the direction that you say Weil proved. | |
| Jul 19, 2013 at 4:32 | comment | added | JSE | Are you asking "what does the actual proof look like" or "how does one know?" Because in practice, "the moduli space of Xes is zero-dimensional" is the same as "all Xes can be defined over number fields" though one has to be careful to massage this into a provable statement. E.G., rigid things like finite etale covers of a fixed curve (e.g. P^1 - 0,1,oo) or elliptic curves with complex multiplication are defined over number fields. | |
| Jul 19, 2013 at 3:32 | comment | added | Igor Rivin | Check out this nice expose: arxiv.org/abs/math/0108222 | |
| Jul 19, 2013 at 1:35 | comment | added | Felipe Voloch | OK. Belyi's theorem is usually stated as an if and only if. The easier direction was actually proved earlier by Weil. | |
| Jul 19, 2013 at 1:10 | comment | added | John Pardon | No, Belyi's theorem is the converse to the OP's statement. (and, yes, I agree Deligne is discussing unramified covers) | |
| Jul 19, 2013 at 1:06 | comment | added | Felipe Voloch | No, this is Belyi's theorem. He is talking about unramified covers. | |
| Jul 19, 2013 at 0:52 | history | edited | Colin McLarty | CC BY-SA 3.0 |
Add the obvious point about meeting some polynomialconditions, as well avoiding others.
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| Jul 18, 2013 at 23:57 | history | asked | Colin McLarty | CC BY-SA 3.0 |