Dimension filtration of the bounded Derived category of a Noetherian ring [PDF]
Let $A$ be a Noetherian ring of dimension $d$ and let $\mathcal{D}^b(A)$ be the bounded derived category of $A$. Let $\mathcal{D}_i^b(A)$ denote the thick subcategory of $\mathcal{D}^b(A)$ consisting of complexes $\mathbf{X}_\bullet$ with $\dim H^n(\mathbf{X}_\bullet) \leq i$ for all $n$. Set $\mathcal{D}_{-1}^b(A) = 0$. Consider the Verdier quotients $
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