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A vanishing theorem for formal cohomology of perverse sheaves. (English) Zbl 0928.32010

From the abstract: “Let \(X\) be an \(n\)-dimensional complex Stein manifold and \(F\) be a perverse sheaf on \(X\). The main result of this paper is that the complex of formal cohomology \({\text R} \Gamma_{C} (X;F \otimes^{W}{\mathcal{O}}_{X})[n]\) 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 Cartan’s Theorem B”.

MSC:

32L20 Vanishing theorems
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