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Canonical transformations and specialization for filtered $${\mathcal D}$$-modules. (Transformations canoniques et spécialisation pour les $${\mathcal D}$$-modules filtrés.) (French) Zbl 0591.14012
Systèmes différentiels et singularités, Colloq. Luminy/France 1983, Astérisque 130, 56-129 (1985).
[For the entire collection see Zbl 0559.00004.]
The aim of this paper is to interpret the theory of analytic microlocalization in the framework of algebraic geometry. Using his former results about algebraic filtered $${\mathcal D}$$-modules, the author studies direct and inverse images of $${\mathcal D}$$-modules, canonical transformation and he relies specialization of a $${\mathcal D}$$-module to normal cone deformation. Then he defines in a new way the characteristic varieties of the second microlocalization. The paper ends with an algebraic construction of formal microdifferential operators.
Reviewer: Y.Laurent

##### MSC:
 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 58J10 Differential complexes 32L99 Holomorphic fiber spaces 13N05 Modules of differentials