Timeline for effective descent of coherent sheaves
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4 at 17:44 | vote | accept | KAK | ||
| Dec 4 at 17:44 | vote | accept | KAK | ||
| Dec 4 at 17:44 | |||||
| Dec 4 at 15:55 | vote | accept | KAK | ||
| Dec 4 at 15:55 | |||||
| Dec 4 at 15:54 | vote | accept | KAK | ||
| Dec 4 at 15:55 | |||||
| Dec 4 at 14:05 | comment | added | Piotr Achinger | Freeness ensures that $X\times_{X/G} X \simeq G\times X$, so that descent data for $X\to X/G$ correspond to $G$-equivariant structures. Then flatness of $X\to X/G$ gives you effective descent. If the action is not free, you can take the quotient stack $[X/G]$ and then the equivalence in question is (basically) a tautology. | |
| Dec 4 at 13:29 | comment | added | KAK | Thank you for your answer. Does the freeness of the action is optimal situation where we have equality? | |
| Dec 4 at 13:01 | comment | added | Carletto | Sorry. I was implicitly supposing that $G* is finite. | |
| S Dec 4 at 13:00 | review | First answers | |||
| Dec 4 at 13:13 | |||||
| S Dec 4 at 13:00 | history | answered | Carletto | CC BY-SA 4.0 |