Timeline for Question about Immersion
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2019 at 14:00 | review | Close votes | |||
| Aug 25, 2019 at 20:52 | |||||
| Aug 23, 2019 at 13:13 | comment | added | R. van Dobben de Bruyn | Ah sorry, I missed the assumption that $X$ is integral. Then reduced induced works, and $X \to \bar X$ is an open immersion. | |
| Aug 23, 2019 at 13:06 | comment | added | user267839 | Oh I forgot to mention that we endow $X'$ with reduced closed subscheme structure in $Y$. | |
| Aug 23, 2019 at 13:03 | comment | added | R. van Dobben de Bruyn | There is not always a scheme structure on the closure compatible with the one on $X$. However, your question is just one of topology: if $X \subseteq Y$ is 'closed inside open', then it equals $U \cap Z$ for $U$ open and $Z$ closed. We may replace $Z$ by $\bar X$, showing that $X$ is open in $\bar X$. | |
| Aug 23, 2019 at 12:49 | history | asked | user267839 | CC BY-SA 4.0 |