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Let A be a Noetherian ring of dimension d and let Dᵇ (A) be the bounded derived category of A. Let Dᵢᵇ (A) denote the thick subcategory of Dᵇ (A) consisting of complexes X_ with Hⁿ (X_) i for all n. Set D-₁ᵇ (A) = 0. Consider the Verdier quotients Cᵢ (A) = Dᵢᵇ (A) /D₈-₁ᵇ (A). We show for i = 0, , d, Cᵢ (A) is a Krull-Remak-Schmidt triangulated category with a bounded t-structure. We identify its heart. We also prove that if A is regular then Cᵢ (A) has AR-triangles. We also prove that Cᵢ (A) ₀/ = ₈ D₀ᵇ (AP).
Tony J. Puthenpurakal (Mon,) studied this question.