Timeline for Does going-down theorem hold for local homomorphism of finite flat dimension?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2023 at 6:50 | answer | added | Vik78 | timeline score: 1 | |
| Dec 11, 2023 at 20:49 | comment | added | Boris | @Bma Thank you very much for your information and thoughts. | |
| Dec 11, 2023 at 15:20 | comment | added | Bma | The miracle flatness theorem implies that in quite general situations such a map is already flat: en.m.wikipedia.org/wiki/Local_criterion_for_flatness . It's also worth noting that a finitely presented local map of local rings satisfies going down iff the induced map on specs is open. This leads me to think that there is probably a counterexample, though I'm not sure what yet | |
| Dec 11, 2023 at 13:24 | comment | added | Boris | @ Vik78 Thank you very much for your kind help. I noticed that in the counter-example you gave, the Krull dimension drops as we follow the local homomorphism. Is this always true? Thanks. | |
| Dec 11, 2023 at 2:19 | comment | added | Vik78 | The same counterexample I gave for your previous question ($\mathbb{Z}_p \to \mathbb{F}_p$) seems to show the answer is no | |
| Dec 11, 2023 at 1:22 | history | asked | Boris | CC BY-SA 4.0 |