Timeline for Infinitely many number fields of class number 1
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 7 at 22:35 | comment | added | Ian Agol | One can imagine a solution to this problem that is not exactly explicit. By class field theory, the class group of a number field is isomorphic to the Galois group of the maximal unramified abelian extension. One may take this extension, then iterate, taking the maximal unramified abelian extension at each stage. If this process terminates, then the final field has class number one. One can imagine proving finiteness for some class of fields without knowing explicitly the extension. | |
| Jun 5 at 21:27 | vote | accept | Stanley Yao Xiao | ||
| Jun 5 at 21:14 | history | became hot network question | |||
| Jun 5 at 17:20 | comment | added | KConrad | No infinite family has been proved to work, but there are proposed examples of them in $\mathbf Z_p$-extensions: see mathoverflow.net/questions/82480/… including the comments there. | |
| Jun 5 at 13:15 | answer | added | Olivier | timeline score: 20 | |
| Jun 5 at 13:11 | history | asked | Stanley Yao Xiao | CC BY-SA 4.0 |