Timeline for Quasi-compact surjective morphism of smooth k-schemes is flat
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 21, 2021 at 11:23 | comment | added | abx | @Sasha: Very good! | |
| Oct 21, 2021 at 9:07 | comment | added | Sasha | @abx: please, have a look at the new example. | |
| Oct 21, 2021 at 9:07 | history | edited | Sasha | CC BY-SA 4.0 |
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| Oct 20, 2021 at 21:29 | vote | accept | Vanni | ||
| Oct 20, 2021 at 9:49 | comment | added | Sasha | @abx: thanks for pointing this! I will modify my example later. | |
| Oct 20, 2021 at 8:31 | comment | added | abx | But your $X$ is singular at $(0,0)$. | |
| Oct 20, 2021 at 7:09 | comment | added | Sasha | @Vanni: I added to the answer an example of non-flat affine morphism. | |
| Oct 20, 2021 at 7:08 | history | edited | Sasha | CC BY-SA 4.0 |
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| Oct 19, 2021 at 21:19 | comment | added | Vanni | @Ariyan Javanpeykar The version I am referring to is the published one; you can access the relevant part following the link I provided (theorem A.12 is in Appendix B, which can be read online also without accessing the full document); the comments between square brackets are mine. | |
| Oct 19, 2021 at 21:14 | comment | added | Ariyan Javanpeykar | @Vanni I can't find the sentence "is a quasi-compact [even affine] and surjective morphism of smooth 𝑘-schemes [𝑘 is a field] and therefore faithfully flat and locally of finite presentation" in the arXiv version. | |
| Oct 19, 2021 at 20:58 | comment | added | Vanni | @Laurent Moret-Bailly: Are you looking at the ArXiv version or at the published version? The two differ considerably; in the ArXiv version, the result I was referring to is Theorem 12.13. | |
| Oct 19, 2021 at 20:56 | comment | added | Vanni | Sasha: Thank you very much for your answer; do you know any counterexamples in the case the morphism is even affine? | |
| Oct 19, 2021 at 20:35 | comment | added | Laurent Moret-Bailly | I could not find a Theorem A.12 in the reference. | |
| Oct 19, 2021 at 19:59 | history | answered | Sasha | CC BY-SA 4.0 |