Timeline for Descent of coherent sheaves on finite coverings
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2018 at 18:26 | vote | accept | Jana | ||
| Mar 4, 2018 at 17:25 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 2, 2018 at 15:45 | answer | added | Sasha | timeline score: 2 | |
| Jan 31, 2018 at 6:08 | history | undeleted | Jana | ||
| Jan 31, 2018 at 6:07 | history | deleted | Jana | via Vote | |
| Jan 31, 2018 at 4:23 | comment | added | nfdc23 | No: Galois descent is not faithfully flat descent for generically Galois finite flat covers that are not etale. Choose $x \in X$ at which $\pi$ is ramified and let $z=\pi(x)$, so $\{x\}$ is $\sigma$-stable. The inverse ideal sheaf $E=O(x)$ is isomorphic to its own $\sigma$-pullback (even in a manner that restricts to a descent datum over $\mathbf{P}^1-\{z\}$, which you didn't ask to be satisfied but should have required). This $E$ is not the pullback of a vector bundle $F$ on the base, as otherwise $F$ would be a line bundle and $1=\deg(E) = \deg(\pi)\deg(F)=2\deg(F)$ is even, an absurdity. | |
| Jan 31, 2018 at 3:54 | history | asked | Jana | CC BY-SA 3.0 |