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Zbl 0617.32014
Laurent, Y.; Schapira, Pierre
Images inverses des modules différentiels. (Pre-images of differential modules). (French)
[J] Compos. Math. 61, 229-251 (1987). ISSN 0010-437X; ISSN 1570-5846/e

Let Y be a subvariety of an analytic variety (X,${\cal O}\sb X)$, ${\cal M}\sp a $coherend ${\cal D}\sb X$-module and ${\cal D}\sb X$ a sheaf of holomorphic differential operators on X. The authors consider systems induced on Y by ${\cal M}$ using a filtration $F\sb Y{\cal D}\sb X$ associated to Y. They prove that the characteristic variety of induced systems is contained in $T\sp*Y\cap \hat C\sb{T\sb YX}({\cal M})$, and they give a criterion for coherency of induced systems. Finally, if Y is a hypersurface they construct a new microcharacteristic variety which improves results obtained using $\hat C{}\sb{T\sb YX}({\cal M})$.
[R.Salvi]

MSC 2000:: *32C38 Sheaves of differential operators (analytic spaces)
58J10 Differential complexes

Keywords: analytic variety; ${\cal D}\sb X$-module; filtration; characteristic variety; induced systems

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