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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

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