Timeline for Resolving complexes of coherent analytic sheaves
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2022 at 15:02 | vote | accept | Tim | ||
| Dec 7, 2022 at 20:50 | answer | added | Richard Lärkäng | timeline score: 2 | |
| Nov 28, 2022 at 17:14 | comment | added | Z. M | I am not familiar with complex geometry, but there is a stronger form of Oka's coherence for arbitrary compact Stein subsets. See Clausen–Scholze, Complex Thm 10.5 and Thm 10.10. It looks like that then you can pick a compact Stein neighborhood and pick a locally free resolution, just as if it were completely algebraic. | |
| Nov 28, 2022 at 14:23 | history | edited | Tim | CC BY-SA 4.0 |
added 18 characters in body
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| Nov 28, 2022 at 12:43 | comment | added | Tim | so I agree that maybe "much more general" is a small exaggeration, but "more general" is fair, I think, in that it's not just for complex manifolds :-) | |
| Nov 28, 2022 at 12:37 | comment | added | Tim | So the original result in SGA 6, §1 (Corollaire 5.10) is for ringed toposes with enough points and such that all stalks are of finite tor-dimension — the specific example that lets you recover smooth complex manifolds is that of a ringed space with regular local rings. | |
| Nov 28, 2022 at 7:13 | comment | added | Z. M | In the second, what do you mean by "much more" general than smooth manifolds? This equivalence depends on the smoothness (more precisely, the regularity) of the scheme. The two are different if the scheme is only an lci. Furthermore, I did not read SGA, but this seems to be algebraic, not analytic. | |
| Nov 28, 2022 at 1:11 | history | asked | Tim | CC BY-SA 4.0 |