Let M be a coherent module over the ring DX of linear differential operators on an analytic manifold X and let _Z_1 , . . . , Zk be k germs of transverse hypersurfaces at a point x ∈ X. The Malgrange–Kashiwara V-ﬁltrations along these hypersurfaces, associated with a given presentation of the germ of M at x, give rise to a multiﬁltration U•(M) of Mx as in Sabbah’s paper  and to an analytic standard fan in a way similar to . We prove here that this standard fan is adapted to the multiﬁltration, in the sense of C. Sabbah. This result completes the proof of the existence of an adapted fan in , for which the use of  is not possible.
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Francisco J. Castro-Jiménez, Michel Granger, A Flatness Property for Filtered <em>D</em>-modules. Publ. Res. Inst. Math. Sci. 43 (2007), no. 1, pp. 121–141DOI 10.2977/PRIMS/1199403810