Timeline for smoothness of a morphism of schemes
Current License: CC BY-SA 4.0
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| Aug 31, 2019 at 9:26 | comment | added | sky223 | I modified the question for clarity. I would like to know if there exists a non-smooth f which satisfies the criterion on all pairs of trivial extensions ($T',T$) as in the post, or if any morphism that satisfies the lifting property for all such pairs must then satisfy the property on all pairs of 1st order thickenings (and thus must be smooth). As you point out in your example, the singular variety (xy=0) over k doesn't satisfy the lifting property on all pairs of trivial extensions. | |
| Aug 31, 2019 at 0:41 | history | edited | edgarlorp | CC BY-SA 4.0 |
added 62 characters in body
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| Aug 31, 2019 at 0:40 | review | First posts | |||
| Aug 31, 2019 at 0:57 | |||||
| Aug 31, 2019 at 0:36 | history | answered | edgarlorp | CC BY-SA 4.0 |