Timeline for is the category of coherent sheaves some kind of abelian envelope of the category of vector bundles?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2015 at 14:01 | comment | added | Ingo Blechschmidt | This too is not answering the question, but note that -- if $\mathcal{O}_X$ is coherent (for instance, if $X$ is locally Noetherian) -- then $\mathrm{Coh}(X)$ is the smallest abelian subcategory of $\mathrm{Mod}(\mathcal{O}_X)$ containing the locally free $\mathcal{O}_X$-modules in an "indexed"/"fibered" sense, since any coherent sheaf is locally a cokernel of a map between finite locally free modules. (Coherence of $\mathcal{O}_X$ is needed to ensure that finite locally free modules are coherent.) | |
| Dec 7, 2013 at 0:27 | vote | accept | John Salvatierrez | ||
| Nov 30, 2013 at 23:38 | history | edited | John Salvatierrez | CC BY-SA 3.0 |
added 12 characters in body
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| Nov 29, 2013 at 16:19 | comment | added | Lennart Meier | This is not answering your question, but I want to remark that on an arbitrary scheme or algebraic stack not every coherent sheaf is a quotient of a vector bundle: dpmms.cam.ac.uk/~bt219/res.pdf | |
| Nov 28, 2013 at 17:08 | answer | added | Daniel Schäppi | timeline score: 19 | |
| Nov 28, 2013 at 2:44 | answer | added | Qiaochu Yuan | timeline score: 11 | |
| Nov 28, 2013 at 0:34 | answer | added | Eric Wofsey | timeline score: 11 | |
| Nov 27, 2013 at 23:59 | answer | added | ya-tayr | timeline score: 2 | |
| Nov 27, 2013 at 23:36 | answer | added | Anton Fonarev | timeline score: 4 | |
| Nov 27, 2013 at 23:23 | history | asked | John Salvatierrez | CC BY-SA 3.0 |