Let X be a complex analytic manifold. Given a closed subspace Y ⊂ X of pure codimension p ≥ 1, we consider the sheaf of local algebraic cohomology Hp[Y](OX), and L(Y,X)⊂ Hp[Y ](OX) the intersection homology DX-Module of Brylinski-Kashiwara. We give here an algebraic characterization of the spaces Y such that L(Y,X) coincides with Hp[Y](OX), in terms of Bernstein-Sato functional equations.
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Tristan Torrelli, Intersection Homology <i>D</i>-Module and Bernstein Polynomials Associated with a Complete Intersection. Publ. Res. Inst. Math. Sci. 45 (2009), no. 2, pp. 645–660DOI 10.2977/PRIMS/1241553132