Timeline for Is it true that any étale morphism is quasi-affine?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2018 at 12:40 | comment | added | Ariyan Javanpeykar | As Marc Hoyois indicates: a quasi-finite morphism is quasi-affine if and only if it separated. To prove this, you can use ZMT (as he says). Indeed, note that a quasi-finite separated morphism factors as an open immersion and a finite morphism. Since finite morphisms are affine, it follows that every quasi-finite separated morphism is quasi-affine. | |
| Jun 6, 2018 at 11:32 | comment | added | Denis Nardin | Silly example: the line with two origins projecting to $\mathbb{A}^1$ is étale (it's even a local isomorphism!) but it is certainly not quasi-affine | |
| S Jun 6, 2018 at 11:21 | history | suggested | Armando j18eos | CC BY-SA 4.0 |
I had fix some mistake
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| Jun 6, 2018 at 9:44 | review | Suggested edits | |||
| S Jun 6, 2018 at 11:21 | |||||
| Jun 6, 2018 at 0:45 | comment | added | Marc Hoyois | $\phi$ will be quasi-affine iff it is separated, which is not automatic for etale morphisms. The nontrivial implication is Zariski's Main Theorem. | |
| Jun 5, 2018 at 23:17 | history | asked | Rami | CC BY-SA 4.0 |