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For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.

9 votes

Derived categories of (coherent) sheaves of modules: exceptional images, gluing, and proper ...

Briefly re 2 and 4: the Ind-completion IndDCoh has shriek pullbacks and star pushforwards. Moreover, it has what one might call "derived h-" descent with respect to shriek pullback. This includes "d …
Anatoly Preygel's user avatar