Timeline for Which complexes of coherent sheaves are dual to perfect ones?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 23 at 16:00 | comment | added | Leo Alonso | The scheme $X$ is Gorenstein if and only if $\omega_X$ is invertible and it follows that $\mathrm{Perf}(X)\otimes\omega%^{-1} \cong \mathrm{Perf}(X) $ precisely in this case. | |
| Jun 1, 2019 at 14:34 | vote | accept | Mikhail Bondarko | ||
| Jun 1, 2019 at 14:33 | comment | added | Denis Nardin | @MikhailBondarko Regarding your last question: not in general, if $D$ is invertible (wrt to the tensor product), then it is dualizable, and so perfect. | |
| Jun 1, 2019 at 14:30 | comment | added | Mikhail Bondarko | Dear Denis, no, you shouldn't delete this. I am not sure that I understand these matters well; so you answer is quite helpful for me; thank you! Moreover, I do not understand whether $\hat D$ gives a tensor inverse to $D$ in this more general case as well (cf. Greg Stivenson's answer). | |
| Jun 1, 2019 at 11:16 | history | edited | Denis Nardin | CC BY-SA 4.0 |
added 216 characters in body
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| Jun 1, 2019 at 10:33 | comment | added | Denis Nardin | I just noticed that this exact argument is present in the answer you linked, so I am now unsure of what kind of answer you were expecting. Should I delete this? | |
| Jun 1, 2019 at 10:32 | history | answered | Denis Nardin | CC BY-SA 4.0 |