Timeline for On the history of the Artin Reciprocity Law
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2016 at 20:27 | vote | accept | Asvin | ||
| Jul 4, 2016 at 17:53 | comment | added | Franz Lemmermeyer | There are no nonabelian crossings in Chebotarev - the abelian case rules, as in Artin's reciprocity law. I don't think you can modify nonabelian extensions sufficiently using cyclotomic extensions, due to the lack of nontrivial subfields. | |
| Jul 4, 2016 at 5:04 | comment | added | Michael Zieve | Thanks for clarifying that. I guess it still seems reasonable that the method is credited to Chebotarev, since it seems like a leap to go from crossing an abelian extension by a cyclotomic one to crossing a nonabelian by a cyclotomic. | |
| Jul 4, 2016 at 4:35 | comment | added | Franz Lemmermeyer | Hilbert used the basic idea in his proof of the Kronecker-Weber Theorem: for showing that an abelian extension $K/{\mathbb Q}$ is cyclotomic he looked at subfields of composita of $K$ with cyclotomic extensions. | |
| Jul 4, 2016 at 1:23 | comment | added | Michael Zieve | I didn't realize that the argument commonly known as "Chebotarev's field crossing argument" was in fact due to Hilbert! I checked your "Reciprocity Laws" book, but didn't see this discussed there. Could you say more about this? | |
| Jul 3, 2016 at 20:13 | history | answered | Franz Lemmermeyer | CC BY-SA 3.0 |