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Jul 21, 2023 at 12:58 comment added Flavius Aetius @ Zhen Lin, is it true thought for sheaves of fields $\mathbb{F}_X$?
Apr 1, 2022 at 15:19 comment added Grisha Papayanov You're probably aware of this, but if $\mathcal{A}$ has Ext-dimension 1, then every bounded complex splits in the derived category, see e.g. stacks.math.columbia.edu/tag/0GM4
Mar 30, 2022 at 23:34 comment added Sam K Indeed, as this answer states. I'm hoping for possibly more general statements though, if they exist.
Mar 30, 2022 at 23:20 comment added Zhen Lin If $R$ is a field, then in fact it happens always.
Mar 30, 2022 at 23:14 history asked Sam K CC BY-SA 4.0