Timeline for Galois action on posets of number fields and $p$-adic fields
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2018 at 11:38 | history | undeleted | S. Carnahan♦ | ||
| Apr 12, 2018 at 4:04 | history | deleted | user122285 | via Vote | |
| Mar 27, 2018 at 23:04 | comment | added | user122285 | @Filippo Alberto Edoardo, In the case of number fields we, of course, have more to play with since we have an infinite collection of intertwined posets reflecting local-global interactions. | |
| Mar 27, 2018 at 23:01 | comment | added | user122285 | @Filippo Alberto Edoardo, thanks for bringing out the implicit question: how much can be learnt about a group from studying its action on the poset of its subgroups, especially when the poset is topologized, thus bringing cohomological methods in play? | |
| Mar 25, 2018 at 10:05 | comment | added | Filippo Alberto Edoardo | I am definitely not an expert in group actions on posets, but I suspect that nothing interest would come out when applying Galois to the poset of subfields. Every extension $L/Q$ (where $Q=\mathbb{Q}$ or $Q=\mathbb{Q}_p$) which is Galois would be fixed by the action, and more generally every extension $L/Q$ could only be sent to a conjugate $L'$. By the Galois correspondance, this is just a group acting on the poset of its subgroups, which doesn't say much on the group itself, I guess (it is here where I might be wrong). In a way, one is simply studying $G_Q$ by looking at its quotients. | |
| Mar 25, 2018 at 4:08 | history | edited | user122285 | CC BY-SA 3.0 |
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| Mar 25, 2018 at 3:54 | history | edited | user122285 | CC BY-SA 3.0 |
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| Mar 24, 2018 at 23:58 | history | asked | user122285 | CC BY-SA 3.0 |