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)/Dᵢ₋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) _P A/P = i D₀ᵇ(AP).
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Tony J. Puthenpurakal (2024) studied this question.
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