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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

##### MSC:
 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)