Timeline for Condition for a morphism of stacks to be locally of finite type
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 14, 2017 at 12:45 | vote | accept | Andrea Ricolfi | ||
| Mar 13, 2017 at 10:41 | comment | added | Ben Davison | btw you don't need any conditions on $X$ for the statement you want. A morphism $Z\rightarrow [X/G]$ is given by a principal $G$-bundle on $Z$ and a $G$-equivariant map from the total space to $X$. If you take an etale neighbourhood $U$ on which this bundle is trivial, the map of schemes $U\times_{[X/G]} [X/H]\rightarrow U$ becomes $U\times (G/H)\rightarrow U$, which is finite type. | |
| Mar 13, 2017 at 10:37 | comment | added | Ben Davison | I guess above I was using $Y\times_H G$ as an atlas, and reasoning that it was of finite type, but yes, $Y\times G$ also provides a finite type atlas. | |
| Mar 11, 2017 at 13:50 | comment | added | Andrea Ricolfi | Thanks! So, $[(Y\times G)/H]$ is of finite type because $Y\times G\to [(Y\times G)/H]$ is an atlas and $Y\times G$ is of finite type? Or am I misunderstanding your second-last sentence? | |
| Mar 11, 2017 at 13:03 | history | answered | Ben Davison | CC BY-SA 3.0 |