Timeline for Does a section of a morphism of schemes give a subscheme?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2017 at 7:27 | review | Close votes | |||
| Apr 22, 2017 at 11:11 | |||||
| Apr 21, 2017 at 18:00 | comment | added | Marc Hoyois | This is false for algebraic spaces: the diagonal of an algebraic space is not necessarily an immersion. | |
| Apr 21, 2017 at 17:29 | answer | added | Vincenzo Zaccaro | timeline score: 5 | |
| Sep 14, 2013 at 11:07 | review | Close votes | |||
| Sep 14, 2013 at 21:29 | |||||
| Sep 14, 2013 at 10:50 | comment | added | Martin Brandenburg | In general $s$ is a locally closed immersion. This belongs to the basics of AG and can be found everywhere, therefore I have voted to migrate the question to math.SE. | |
| Sep 14, 2013 at 5:49 | comment | added | Kevin Ventullo | Also, if $f$ is not separated, then $s$ need not be a closed immersion (take $X$ to be two affine lines glued away from the origin, and $f$ the projection to a single affine line). | |
| Sep 14, 2013 at 2:34 | comment | added | Kestutis Cesnavicius | If $f$ is separated, then the answer is 'yes': it is a standard fact that if a composition of two morphisms is a closed immersion and the second one is separated, then the first one is also a closed immersion. See Hartshorne's book Exercise II.4.8; if you don't want to do exercises, I'm sure you can also locate this is in EGA without troubles. | |
| Sep 14, 2013 at 0:05 | history | asked | Heer | CC BY-SA 3.0 |