Angéniol, B.; Lejeune-Jalabert, M. Le théorème de Riemann-Roch singulier pour les \({\mathcal D}\)-modules. (French) Zbl 0569.14007 Systèmes différentiels et singularités, Colloq. Luminy/France 1983, Astérisque 130, 130-160 (1985). [For the entire collection see Zbl 0559.00004.] The aim of the paper is to discuss some versions of the Riemann-Roch theorem, especially for \({\mathcal D}\)-modules. After preliminaries on Quillen isomorphisms and de Rham correspondences between various Grothendieck groups, a smooth variant of the Riemann-Roch theorem for \({\mathcal D}\)-modules is deduced from one for \({\mathcal O}\)-modules. Some consequences are given, such as a formula for the index of a holonomic module. The main part of the paper deals with the singular case. The sketch of the proof of the singular analytic version of Riemann-Roch theorem for \({\mathcal D}\)-modules is given. - The end of the paper is devoted to open problems. Reviewer: A.Pankov Cited in 1 Review MSC: 14C40 Riemann-Roch theorems 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results Keywords:singular Riemann-Roch theorem; \({\mathcal D}\)-modules; index of a holonomic module Citations:Zbl 0559.00004 PDFBibTeX XML