Timeline for Free action of finite group on a scheme
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29 at 0:19 | comment | added | Ravi Vakil | @R.vanDobbendeBruyn how is it not citable? | |
| Oct 12 at 7:10 | comment | added | user4231 | In the meantime I found Thm 4.16 in math.ru.nl/~bmoonen/BookAV/Quotients.pdf It is not from a paper or a book, but might be good enough | |
| Oct 10 at 20:39 | comment | added | R. van Dobben de Bruyn | @RaviVakil thanks, but I think mine doesn't fully answer it, so I left a comment. I have the feeling the OP is specifically looking for a citable source, which I'm not sure I can provide. | |
| Oct 10 at 18:51 | comment | added | Ravi Vakil | @R.vanDobbendeBruyn do you want to give that as an answer so it can be accepted? You might mention for the second that $X \rightarrow X/G$ is an $G$-bundle, hence etale-locally of the form $Y \times G \rightarrow Y$, which is finite; and finiteness of morphisms descends under etale maps, thereby answring both questions. | |
| Oct 8 at 16:57 | comment | added | R. van Dobben de Bruyn | In 1, the two conditions are equivalent (even when $X \to S$ is only assumed separated). Indeed, the map you wrote down is a map of schemes over $X$ (via the second projection), where $G \times_S X \to X$ is finite, hence proper. If $Z$ is the scheme-theoretic image, then $G \times_S X \to Z$ is proper [Tag 01W6], hence a closed immersion if it is a monomorphism [Tag 04XV]. | |
| Oct 8 at 15:38 | history | asked | user4231 | CC BY-SA 4.0 |