Timeline for Terminology about ramification
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2019 at 4:50 | comment | added | François Brunault | @EFinat-S You're right, in Serre 2.1 it seems the assumption $S \supset S_\infty$ is missing. I am not familiar enough with the literature to tell whether some authors leave ramification at infinity undefined, which would explain this. | |
| Apr 22, 2019 at 15:19 | comment | added | efs | @FrançoisBrunault I'm aware of ramification at infinite places. For example, Serre talks about places, and that's exactly what confusses me. I know it's a detail, but I want to understand this correctly. | |
| Apr 22, 2019 at 7:53 | comment | added | François Brunault | Ramification at the infinite places has its own definition, so when $K=\mathbf{Q}$ and $S$ is a finite set of prime numbers, some authors may implicitly consider that $\mathbf{Q}_S$ is the maximal abelian extension of $\mathbf{Q}$ unramified at each finite prime $q \not\in S$. So things may depend whether $S$ is a set of primes or a set of places. I agree that it should be said explicitly though. | |
| Apr 20, 2019 at 18:40 | comment | added | efs | @KConrad Sorry, I hope now is ok. | |
| Apr 20, 2019 at 18:40 | history | edited | efs | CC BY-SA 4.0 |
deleted 15 characters in body
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| Apr 20, 2019 at 18:27 | comment | added | KConrad | Please put actual article references in the post, not just links. When I click on the first link, I am sent to Google Books and it tells me in Spanish that I've reached my page limit. | |
| Apr 20, 2019 at 16:04 | history | edited | efs | CC BY-SA 4.0 |
links added
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| Apr 20, 2019 at 15:54 | comment | added | efs | @KConrad I'll put the links in my question. | |
| Apr 20, 2019 at 6:41 | comment | added | KConrad | When $S$ is a finite set of places that does not mean it must contain $S_\infty$. Yet often in practice it does contain $S_\infty$ and this restriction should be explicitly stated when it occurs. Are you sure you're not overlooking some convention earlier in a paper that would imply the sets $S$ in the paper will always contain $S_\infty$? Please give some examples of papers where you think the author (say Serre) is forgetting to say $S \supset S_\infty$. | |
| Apr 19, 2019 at 15:07 | history | asked | efs | CC BY-SA 4.0 |