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 | |
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| Dec 12, 2023 at 17:54 | comment | added | Boris | I see. Thank you very much for the counter-example. | |
| Dec 12, 2023 at 15:56 | comment | added | Vik78 | No, by the Auslander-Buchsbaum theorem the map $\mathbb{C}[x]_{(x)} \to \mathbb{C}[x, y]_{(x,y)}$ is a counterexample | |
| Dec 12, 2023 at 13:41 | comment | added | Boris | Thank you so much for your detailed answer. I would like to ask is it true in general that if $f:A\rightarrow B$ is a local homomorphism of finite flat dimension between Noetherian local rings, then dimension of $A$ is always at least dimension of $B$? Thanks. | |
| Dec 12, 2023 at 7:26 | history | edited | Vik78 | CC BY-SA 4.0 |
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| Dec 12, 2023 at 7:13 | history | edited | Vik78 | CC BY-SA 4.0 |
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| Dec 12, 2023 at 6:50 | history | answered | Vik78 | CC BY-SA 4.0 |