Timeline for Is the Serre dualizing complex local in the analytic topology?
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| Jan 14, 2022 at 12:57 | comment | added | Dmitry Vaintrob | @JasonStarr Thank you! I had trouble finding the local cohomology identification (the pdf I have isn't easily searchable). But I'm pretty sure you're right. One argument to see this is to interpret the Serre dualizing complex using Verdier duality of holonomic D modules, which can be done in the analytic topology. | |
| Jan 13, 2022 at 11:54 | comment | added | Jason Starr | In Hartshorne's "Residues and Duality", there is a characterization of the (quasi-isomorphism class) of the stalks of the dualizing sheaf in terms of local cohomology. That should still work in the analytic category. Obviously when you choose $U$ to be all of $X$, the analytic and algebraic (bounded) derived categories of coherent are equal, so in that case you also have a characterization that works in the analytic category. This same question must arise for rigid analytic spaces, so perhaps you could search for dualizing complexes of rigid analytic spaces. | |
| Jan 13, 2022 at 11:26 | history | asked | Dmitry Vaintrob | CC BY-SA 4.0 |