Timeline for Generalizations of Belyi's theorem
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2010 at 8:51 | vote | accept | Marc Palm | ||
| Nov 16, 2010 at 17:53 | comment | added | Emerton | The preceding comment should actually explains not the equivalence of (2) and (3), but rather the equivalence of (3) and (2'), where (2') is the statement that $X$ can be written as a cover of $\mathbb P^1$ unramified outside 3 points (which one can take to be $0,1,\infty$). The equivalence of (1) and (2') is what I usually think of as being Belyi's theorem. | |
| Nov 16, 2010 at 17:48 | comment | added | Emerton | The equivalence of (2) and (3) follows from the fact that the upper half-plane mod $\Gamma_1(4)$ (for example) is equal to $\mathbb P^1 \setminus \{0,1,\infty\}$, and hence giving a finite degree cover of $\mathbb P^1$ unramified outside $0,1,\infty$ is the same as giving a finite index subgroup of $\Gamma_1(4)$. | |
| Nov 16, 2010 at 17:17 | comment | added | Marc Palm | Okay, that was also what I suspected! Thanks for the reference, although it just threats 1<=>2. – Marc 0 secs ago | |
| Nov 16, 2010 at 17:08 | history | answered | Robin Chapman | CC BY-SA 2.5 |