Timeline for Kähler differential of completion of algebra
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2020 at 13:02 | comment | added | Piotr Achinger | nothing particularly useful. We know that $k[[x]]$ is the increasing union of smooth $k[x]$-algebras (by Neron desingularization) which seems to show that $\Omega^1_{k[[x]]}$ is free of infinite rank. I don't know what you want to do with it but it's probably the wrong object to look at. | |
| May 11, 2020 at 12:40 | comment | added | Sunny | Ok got it. Can you tell me what is $\Omega^{1}_{k[[x]]}$? | |
| May 11, 2020 at 7:21 | comment | added | Piotr Achinger | No, this is already false for $R = k[t]_{(t)}$, $\widehat{R} = k[[t]]$, because the equation $d(\sum a_n t^n) = \sum n a_n t^{n-1}$ holds in the target but not in general in the source (N.B. your map goes in the wrong way). That's why for complete rings one usually works with continuous differentials rather than Kahler differentials. | |
| S May 11, 2020 at 7:14 | history | suggested | user142929 | CC BY-SA 4.0 |
Edited title.
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| May 11, 2020 at 6:51 | review | Suggested edits | |||
| S May 11, 2020 at 7:14 | |||||
| May 11, 2020 at 6:45 | history | asked | Sunny | CC BY-SA 4.0 |