Spécialisation de faisceaux et monodromie modérée. (French) Zbl 0532.14008

Verdier, J. L.

Astérisque 101-102, 332-364 (1983).

Given an analytic subspace Y of an analytic space X, this paper defines in an intrinsic way a ”specialization” functor \(Sp_{Y\backslash X}:D_{const}(X)\to D_{const}(C_{Y\backslash X})\) from the (derived) category of constructible sheaves on X to the (derived) category of constructible sheaves on the normal cone to Y in X; the sheaves thus obtained are locally constant along the punctured generatrices of the normal cone, and in the special case of a divisor Y defined by a local equation f they correspond to Deligne’s ”sheaves of vanishing cycles” \(R^ i\psi_ f\). - The p characteristic and the complex case are discussed separately.
For the entire collection see [Zbl 0515.00021].

Reviewer: F.Pham

MSC:

14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
14F40	de Rham cohomology and algebraic geometry
14F25	Classical real and complex (co)homology in algebraic geometry
32L10	Sheaves and cohomology of sections of holomorphic vector bundles, general results
32C25	Analytic subsets and submanifolds

Keywords:

monodromy; perverse sheaves; specialization functor on constructible sheaves; sheaves of vanishing cycles