A Flatness Property for Filtered -modules

  • Francisco J. Castro-Jiménez

    Universidad de Sevilla, Spain
  • Michel Granger

    Université d'Angers, France


Let be a coherent module over the ring of linear differential operators on an analytic manifold and let be germs of transverse hypersurfaces at a point . The Malgrange–Kashiwara -filtrations along these hypersurfaces, associated with a given presentation of the germ of at , give rise to a multifiltration of as in Sabbah’s paper [9] and to an analytic standard fan in a way similar to [3]. 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 [9], for which the use of [8] is not possible.

Cite this article

Francisco J. Castro-Jiménez, Michel Granger, A Flatness Property for Filtered -modules. Publ. Res. Inst. Math. Sci. 43 (2007), no. 1, pp. 121–141

DOI 10.2977/PRIMS/1199403810