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The local duality theorem in $${\mathcal D}$$-module theory. (English) Zbl 1061.32007
Elements of the theory of geometric differential systems. Papers from the C.I.M.P.A summer school, Séville, Spain, September 1996. Paris: Société Mathématique de France (ISBN 2-85629-151-1/pbk). Séminaires et Congrès 8, 59-87 (2004).
The author gives an introduction to the local duality theorem in $${\mathcal D}$$-module theory (that is, that the Grothendieck-Verdier duality for analytic constructible complexes interchanges the de Rham complex and the solution complex of holonomic modules over a complex analytic manifold), and carefully explains its proofs given by Z. Mebkhout in: These de Doctorat d’Etat. Specialite: Mathematiques. Universite de Paris VII. 128 p. (1979; Zbl 0455.32006) and by M. Kashiwara and T. Kawai given in Publ. Res. Inst. Math. Sci. 17, 813–979 (1981; Zbl 0505.58033).
For the entire collection see [Zbl 1050.32001].

##### MSC:
 32C38 Sheaves of differential operators and their modules, $$D$$-modules 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
##### Keywords:
de Rham complex; Grothendieck-Verdier duality