Timeline for Vanishing of Kahler differentials vs. surjective Frobenius?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 15, 2021 at 13:41 | comment | added | user267839 | I think the proof of these equivalences might provide a direct way to show the known fact that if $A$ field extension of $k$ then $A \otimes A$ reduced iff $I=I^2$ (related to my question here: math.stackexchange.com/questions/4225005/…). By "direct" I mean that I know several proofs deducing this fact from well known exact sequences between Kahler differentials, but I"m curious if it also possible to give a direct "minimalistic" proof of the claim only working with properties of $I$. | |
| Aug 15, 2021 at 13:12 | comment | added | user267839 | Could you give a reference where a proof can be found that all these four conditions are equivalent? | |
| Jun 8, 2016 at 2:19 | comment | added | Qiaochu Yuan | @Ben: yes, I mentioned that in the argument. | |
| Jun 7, 2016 at 19:55 | comment | added | David Benjamin Lim | I don't think that $\Omega^1_{A/k} = 0$ implies that $A$ is separable over $k$, we need to add some finiteness hypotheses (like say $A$ f.t. over $k$). | |
| Jun 7, 2016 at 7:10 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jun 7, 2016 at 7:02 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jun 7, 2016 at 6:55 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |