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Le réseau $$L^ 2$$ d’un système holonome régulier. (The $$L^ 2$$- réseau of a regular holonomic system). (French) Zbl 0598.32014
The purpose of this paper is to define an $$''L^ 2$$-réseau” of a regular holonomic $${\mathcal D}_ X$$-module on a smooth complex variety and give some applications of it. Let X be a smooth complex variety, Y a closed analytic subset of pure codimension in X and S a hypersurface in Y such that Y-S is non-singular. For a regular holonomic $${\mathcal D}_ X$$- module $${\mathcal M}$$ whose support is contained in Y, we may define a canonical sub $${\mathcal O}_ X$$-module of $${\mathcal M}$$ associated to the $$L^ 2$$-extension. We call it the $$L^ 2$$-réseau and denote it by $$L^ 2(Y,{\mathcal M})$$. In particular, when $$Y=X$$ and $${\mathcal M}$$ has no non-trivial section supported in S, the $$L^ 2$$-réseau contains the réseau of Deligne. By using $$L^ 2(X,{\mathcal M})$$, the author discusses a condition in order that $${\mathcal M}$$ is generated by a ”standard” distribution on X.
Reviewer: M.Muro

##### MSC:
 32C15 Complex spaces 32C25 Analytic subsets and submanifolds 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32C36 Local cohomology of analytic spaces
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