A Vanishing Theorem for Formal Cohomology of Perverse Sheaves

LetXbe an-dimensional complex Stein manifold andFbe a perverse sheaf onX. The main result of this paper is that the complex of formal cohomology RΓc(X; F⊗wOX) [n] is concentrated in degree zero. This result relies on some preliminaries which may have their own interest: flatness of the sheaf of holomorphic tempered functions and a tempered version of Cartanʹs Theorem B.