A Vanishing Theorem for Formal Cohomology of Perverse Sheaves
✍ Scribed by Olivier Berni
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 321 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
Let X be a 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 R1 c (X; F w 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. 1998 Academic Press Contents. Introduction. 1. Notations and review. 2. Tempered cohomology and flatness. 2.1. Review: Siu and Ho rmander Theorems. 2.2. The sheaf O t&U X . 2.3. Flatness and applications. 2.4. Tempered Theorem B and applications. 3. Topology on the space of sections of a D X -module. 3.1. Spaces of type FS and DFS and LF. 3.2. Topology on sections of coherent O X -modules. 3.3. Topology on sections of coherent D X -modules. 4. Topological duality and vanishing theorem. 5. Another proof of Theorem 4.4.
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