Timeline for Algebraically characterizing morphisms of commutative rings that are a homeomorphism on the prime spectra
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2022 at 23:48 | history | edited | Karl Schwede | CC BY-SA 4.0 |
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| Jan 27, 2022 at 23:42 | history | edited | Karl Schwede | CC BY-SA 4.0 |
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| Jan 27, 2022 at 23:27 | comment | added | Karl Schwede | You are right, I screwed that up. Sorry. I will fix that. | |
| Jan 26, 2022 at 22:31 | comment | added | R. van Dobben de Bruyn | If you ask that $\operatorname{Spec} S \to \operatorname{Spec} R$ induces isomorphisms on residue fields and is universally a homeomorphism, then the criterion is somehow the opposite of what you wrote: $S$ is iteratively generated by adjoining elements $x_i$ such that $x_i^2,x_i^3 \in R[x_1,\ldots,x_{i-1}]$. See Tag 0CND. | |
| Jan 26, 2022 at 20:16 | comment | added | Will Sawin | The characterization of subintegral sounds wrong to me. If we take $R = k[x^2, x^3]$ and $S= k[x]$ then the condition in terms of elements is not satisfied but the map is a bijection on prime spectra with the extensions of residue fields all isomorphisms. On the other hand if $R$ and $S$ are fields then the condition in terms of elements is always satisfied but the extension of residue fields is usually not an isomorphism. | |
| Jan 26, 2022 at 20:09 | history | edited | Karl Schwede | CC BY-SA 4.0 |
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| Jan 26, 2022 at 19:47 | history | answered | Karl Schwede | CC BY-SA 4.0 |