an:03843896
Zbl 0532.14008
Verdier, J. L.
Sp??cialisation de faisceaux et monodromie mod??r??e
FR
Ast??risque 101-102, 332-364 (1983).
1983
a
14F05 14F40 14F25 32L10 32C25
monodromy; perverse sheaves; specialization functor on constructible sheaves; sheaves of vanishing cycles
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].
F.Pham