Timeline for Which abelian groups are $\varprojlim^1$ groups?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2020 at 18:01 | vote | accept | Tim Campion | ||
| Oct 9, 2020 at 19:16 | answer | added | Denis T | timeline score: 14 | |
| Oct 9, 2020 at 18:53 | comment | added | Tim Campion | @DenisT. Excellent, thank you -- this would make a great answer! How does one see this / where can I read about it? | |
| Oct 9, 2020 at 18:48 | comment | added | Denis T | Values of lim^1 are precisely cotorsion groups, i. e. ones with $Ext(\Bbb Q, G) = 0$. Values of lim^1 on a tower of f.g. groups are of the form $Ext(A, \Bbb Z)$ with A flat. | |
| Oct 9, 2020 at 17:53 | comment | added | Tim Campion | @MaximeRamzi Thanks, I had some idea like that bouncing around in the back of my head, but I wasn't sure if there were finiteness / connectivity assumptions involved. | |
| Oct 9, 2020 at 17:52 | comment | added | Maxime Ramzi | Question 3 is equivalent to Question 2, as any chain complex of abelian groups is formal (because $\mathbb Z$ is a PID) : there is a zigzag of quasi-isomorphisms $C\to \bigoplus_n H_n(C)[n]$, so the answer to 3 is yes if and only if the answer to 2 is yes for $H_0(C),H_1(C)$ | |
| Oct 9, 2020 at 17:40 | comment | added | Tim Campion | @JeremyRickard Ah, of course you're right. Maybe there isn't really an interesting question to ask at that level of generality... | |
| Oct 9, 2020 at 17:37 | history | edited | YCor |
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| Oct 9, 2020 at 17:37 | comment | added | Jeremy Rickard | For Question 4, can't you just take the constant inverse system with $D^{n,*}=\mathcal{D}^*$ for all $n$? | |
| Oct 9, 2020 at 17:26 | history | asked | Tim Campion | CC BY-SA 4.0 |