Timeline for Class field towers
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2015 at 13:19 | comment | added | user6976 | @quid Yes, it is the same paper, published in Abh. Math. Semin. Univ. Hambg. (2009) 79: 165–187. | |
| Apr 24, 2015 at 13:14 | comment | added | user9072 | @MarkSapir I agree the situation is not clear-cut, which is why I only mentioned the resource rather than answering your question directly. (I also replaced the link there; if you have a moment could you perhaps double check we found the same paper, so that I do not add a wrongish link.) | |
| Apr 24, 2015 at 12:48 | comment | added | user6976 | @quid I looked at that discussion. As far as I understand from Lemmermeyer's paper (the link on that page is broken, but I found the paper anyway), it is more about ideals and their unique prime decompositions, i.e., class number 1, than about general class number. It is good to know that reciprocity laws played important role in the development of the theory of ideal numbers. I did not know that before. FLT also played a role, whether decisive or not - it is not that important to me. | |
| Apr 24, 2015 at 0:57 | comment | added | user9072 | @MarkSapir there is a question by Emerton, with an answers by Lemmermeyer and others, on the relative importance of FLT and reciprocity laws for Kummer's work that contains some information related to this. | |
| Apr 23, 2015 at 21:50 | history | edited | user6976 | CC BY-SA 3.0 |
Corrected a misprint in the second line.
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| Apr 23, 2015 at 21:08 | comment | added | user6976 | Thank you! It does make sense. But at least FLT was the main reason for defining the class number. Right? | |
| Apr 23, 2015 at 20:53 | comment | added | Olivier | @MarkSapir Hilbert care about class fields because it is easier to prove reciprocity laws at primes splitting completely (and that's why he introduced the class field as field in which principal ideals split completely, and not as an unramified extension as we do today). As I learned from Franz Lemmermeyer (which is the go to guy for these questions), from that it is rather natural to ask what is the class group of a Hilbert class field (because if the Hilbert class field is factorial, then all the better for the proof) and whence the class field tower problem. FLT has nothing to do with it. | |
| Apr 23, 2015 at 20:15 | comment | added | user6976 | The question was more about motivation. I always thought that FLT was the motivation for the class tower problem. But it looks like there is no close relation. | |
| Apr 23, 2015 at 18:42 | comment | added | Olivier | @MarkSapir No problem, I'm always happy to squash the hope of proving FLT by elementary means ;-). | |
| Apr 23, 2015 at 15:03 | history | edited | Olivier | CC BY-SA 3.0 |
Improved syntax.
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| Apr 23, 2015 at 14:50 | vote | accept | CommunityBot | moved from User.Id=6976 by developer User.Id=69903 | |
| Apr 23, 2015 at 14:03 | history | answered | Olivier | CC BY-SA 3.0 |