Une démonstration du théorème de dualité de Verdier
type: Item
instance of: scholarly article
title: Une démonstration du théorème de dualité de Verdier
zbMATH Open document ID: 0612.55005
author: Pierre-Paul Grivel
published in: L'Enseignement Mathématique. 2e Série
publication date: 1985-01-01T00:00:00Z
review text: The aim of this paper is to supply a detailed proof of the following theorem announced by \textit{J.-L. Verdier} [Sémin. Bourbaki 1965/1966, Exp. No.300 (1966; Zbl 0268.55006)]: Let \(f: X\to Y\) be a continuous map between two locally compact topological spaces X and Y, and let \({\mathbb{R}}f_ !: D(X)\to D(Y)\) and \(f^ !: D(Y)\to D(X)\) be the functors defined on the derived categories of complexes of R-modules (with R a fixed commutative noetherian ring), which extend the usual images of sheaves. Then, if \(f_ !\) is of finite cohomological dimension, there is a functorial isomorphism \({\mathbb{R}} Hom^.({\mathbb{R}}f_ !(A^.);B^.)={\mathbb{R}}f_* {\mathbb{R}} Hom^.(A^.;f^ !(B^.))\) in \(D^+(Y)\), where \(A^.\in Ob D^-(X)\) and \(B^.\in Ob D^ b(Y)\).
Mathematics Subject Classification ID: 55N30
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 55M05
Mathematics Subject Classification ID: 14F10
zbMATH DE Number: 3990381
zbMATH Keywords: intersection homology
zbMATH Keywords: D-modules
zbMATH Keywords: Verdier duality
zbMATH Keywords: locally compact topological spaces
zbMATH Keywords: derived categories
zbMATH Keywords: cohomological dimension
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3990381