On the derived category of perverse sheaves. (English) Zbl 0652.14008

Beilinson, A. A.

\(K\)-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)

Keywords:

complexes of D-modules; holonomic cohomology; middle perverse sheaves

Citations:

Zbl 0621.00010