Timeline for $M^\wedge_I \to N^\wedge_I$ an isomorphism if $S_P^{-1}M^\wedge_P \to S_P^{-1}N^\wedge_P$ is an isomorphism for all primes $P$ containing $I$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 13, 2023 at 10:40 | comment | added | Z. M | I am not satisfied with this generality. For example, what happens if we remove the Noetherianness, and replace classical completion by derived completion (which is the completion in stable homotopy theory), say. The proof in that paper does not seem to be conceptual enough, either. | |
| Jan 13, 2023 at 10:34 | comment | added | Motmot | Thanks! It's simple in hindsight. If you want to write this as an answer to the question I'll choose it as the accepted answer. | |
| Jan 13, 2023 at 10:03 | comment | added | Z. M | In that case, the completion is an exact functor, thus commutes with taking kernel and cokernel, and you reduce to the case in that paper (btw, you misspelled Adams). | |
| Jan 13, 2023 at 7:54 | comment | added | Motmot | @Z.M yes, I'd assume the same | |
| Jan 12, 2023 at 18:51 | comment | added | Z. M | I look at their paper, and they are assuming that this is a pro-system of finitely generated modules. Would you assume the same? | |
| Jan 12, 2023 at 14:40 | history | asked | Motmot | CC BY-SA 4.0 |