Une démonstration du théorème de dualité de Verdier
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 \(B^.\in Ob D^ b(Y)\).
scientific article; zbMATH DE number 3990381