Timeline for descent for birational morphisms
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2014 at 14:47 | comment | added | user45766 | @finite: Existence of vector bundles and global resolutions for singular surfaces. Compositio Math. 140 (2004), 717-728. Proposition 1.2 | |
| Feb 11, 2014 at 18:37 | comment | added | boxdot | @Aleksa: Unfortunately, I am too stupid to see how you conclude the equivalence of the above categories from the Formal Function Theorem (4.1.5). Could you please say a few words about this? | |
| Jan 31, 2014 at 16:22 | answer | added | Sasha | timeline score: 6 | |
| Jan 31, 2014 at 14:02 | comment | added | Damian Rössler | Also notice that every birational morphism in your setting is a blowing-up along some (possibly non-reduced ...) closed subscheme (see for instance Liu's book, chap. 8, Th. 1.24). | |
| Jan 31, 2014 at 13:57 | comment | added | Jason Starr | Something about the formulation certainly must be changed, because the center $Z\subset Y$ can have nontrivial locally free sheaves. If $\mathcal{F}$ is a locally free sheaf on $Y$ whose restriction to $Y_{/Z}$ is nontrivial, then certainly the restriction of $f^*\mathcal{F}$ to $X_{/E}$ will also be nontrivial. If there is a result of the type you want, I suspect it will be found in Michael Artin's, "Algebraization of Formal Moduli, II". | |
| Jan 31, 2014 at 11:00 | history | asked | Aleksa | CC BY-SA 3.0 |