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On the derived category of perverse sheaves. (English) Zbl 0652.14008
\(K\)-theory, arithmetic and geometry, Semin., Moscow Univ. 1984-86, Lect. Notes Math. 1289, 27-41 (1987).
[For the entire collection see Zbl 0621.00010.]
Let X be a scheme, D the derived category of \({\mathbb{Q}}_{\ell}\)-sheaves on X and M the subcategory of middle perverse sheaves. The author shows that the functor from the derived category of M to D is an equivalence. This is used to obtain the direct image functor on M as a derived functor. There is an analogue for algebraic holonomic \({\mathcal D}\)-modules. There is an appendix on realizing the derived category of the heart of a t-category.
Reviewer: G.Horrocks

14F30 \(p\)-adic cohomology, crystalline cohomology
18F30 Grothendieck groups (category-theoretic aspects)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
14A20 Generalizations (algebraic spaces, stacks)