Timeline for Which properties of a variety are detected by its derived category of coherent sheaves?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2016 at 15:43 | vote | accept | Jan Grabowski | ||
| Jan 17, 2015 at 3:11 | history | edited | Wai-kit Yeung | CC BY-SA 3.0 |
added 113 characters in body
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| Jan 16, 2015 at 11:29 | comment | added | Fernando Muro | @waikit as Adeel says, although at the higher categorical level $D(QCoh(X))$ is the free cocompletion of $D^b(Coh(X))$ at the triangulated level there's no notion of cocompletion. However there are still open questions in this direction, like the Margolis Conjecture, which is the analogue of this in stable homotopy theory mathoverflow.net/questions/67227/… | |
| Jan 12, 2015 at 17:21 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jan 12, 2015 at 14:31 | comment | added | AAK | As far as I know, it is not possible to recover the derived category of quasi-coherent complexes from the bounded derived category of coherent sheaves, at the triangulated level. At the level of infinity- or dg-categories, one can recover it as the ind-objects (in the regular case). | |
| Jan 12, 2015 at 14:01 | comment | added | Wai-kit Yeung | Thanks for the correction. Can the argument be fixed by reconstructing $D(QCoh(X))$ from $D^b(Coh(X))$? Perhaps by defining it as the collection of formal cones of direct sums of object in $D^b(Coh(X))$? | |
| Jan 12, 2015 at 13:57 | comment | added | Jan Grabowski | Thanks @waikit - they are definitely along the lines I had in mind. | |
| Jan 12, 2015 at 13:52 | comment | added | Fernando Muro | 3. is slightly different: $X$ is regular iff $D^b(Coh(X))\subset D(QCoh(X))$ is the subcategory of compact objects. | |
| Jan 12, 2015 at 13:46 | review | First posts | |||
| Jan 12, 2015 at 13:53 | |||||
| Jan 12, 2015 at 13:43 | history | answered | Wai-kit Yeung | CC BY-SA 3.0 |