Timeline for Local factors determine Weil representations - proof of the cyclic case
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2018 at 19:58 | history | bounty ended | Diglett | ||
| Oct 7, 2018 at 19:58 | vote | accept | Diglett | ||
| Oct 7, 2018 at 0:23 | comment | added | Alex B. | If a representation factors through a finite quotient, then you can lift it to the Weil group, but you can also lift it to the full Galois group. Moreover, the former lift will be the restriction of the latter. So I guess I showed that the whole lift to the full Galois group will already be determined by the local polynomial. But really, that distinction is empty for representations that factor through a finite quotient. | |
| Oct 6, 2018 at 22:31 | comment | added | Diglett | Thank you for your response! Most things became much clearer for me now. I still have a question left: Can you also argue with Galois groups $\operatorname{Gal}(\bar{K}/K)$, $\operatorname{Gal}(\bar{K}/L)$ etc. if we do have Weil representations (which was required) instead of Galois representations (as you did)? I just know that the Weil group is a proper subgroup of the absolute Galois group. | |
| Oct 6, 2018 at 1:00 | history | answered | Alex B. | CC BY-SA 4.0 |