Timeline for A misunderstanding about the Moret Bailly theorem
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2010 at 18:55 | comment | added | Kevin Buzzard | Yes definitely the $S_i$ must be finite! The theorem is completely false otherwise---just take a standard counterexample to the Hasse principle like $3x^3+4y^3+5z^3=0$. | |
| Nov 29, 2010 at 18:46 | comment | added | Makhalan Duff | Well, if S_2 is the set of all finite places, and you have a number field unramified over all of S_2, then that number field must equal Q. My guess is Brian's right. | |
| Nov 29, 2010 at 18:41 | comment | added | Kevin Buzzard | If this is the usual Moret-Bailly result that these modularity lifting theorem guys apply, then all it says is that there is a K-point for some number field K in which all primes in a given finite set split. It certainly can't control the degree of K. | |
| Nov 29, 2010 at 18:35 | comment | added | Makhalan Duff | No, but that would make sense. | |
| Nov 29, 2010 at 18:29 | comment | added | BCnrd | The two sets $S_i$ should be finite if I remember correctly. Have you looked at the original paper where Moret-Bailly proved his result? | |
| Nov 29, 2010 at 18:21 | history | asked | Makhalan Duff | CC BY-SA 2.5 |