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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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