Timeline for When adic completion preserves projectives?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2020 at 19:22 | comment | added | Denis T | @PavelČoupek I double-checked my "proof" that this implies L-ness and found an error. Nevertheless, every commutative example I know so far is perfect+coherent. | |
| Nov 4, 2020 at 14:58 | comment | added | Pavel Čoupek | Regarding the PS: From the context it seems that you suggest that "projectives closed under arbitrary limits" implies that $R$ is an L-ring. Why is that? The standard way to get completion is to take an inverse limit over certain quotients, which will typically not be projective themselves... | |
| Nov 4, 2020 at 12:14 | history | edited | Denis T | CC BY-SA 4.0 |
added 159 characters in body
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| Nov 4, 2020 at 10:58 | comment | added | Denis T | Well, yeah, of course. My "not look like that" included being not artinian, so we have some actual completion going on, and preserving projectives is not super obvious. | |
| Nov 4, 2020 at 9:35 | comment | added | Jeremy Rickard | In response to the P.S., $k[x]/(x^2)$, where $k$ is a field, is an example that is right perfect and left coherent, but has infinite global dimension. | |
| Nov 4, 2020 at 8:48 | history | asked | Denis T | CC BY-SA 4.0 |