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Oct 22, 2022 at 6:11 comment added Z. M I want to add that this sort of construction does not adapt to derived categories: $D(R/I)$ is not a full subcategory of $D(A)$. It is also unclear what the product of two (quasi-)ideals is in derived geometry.
Nov 8, 2010 at 19:50 history answered Martin Brandenburg CC BY-SA 2.5