manuscripta mathematica

, Volume 50, Issue 1, pp 49–71

Sur les Images Directes deD-Modules


  • Bernard Malgrange
    • Institut FourierUniversité de Grenoble I

DOI: 10.1007/BF01168827

Cite this article as:
Malgrange, B. Manuscripta Math (1985) 50: 49. doi:10.1007/BF01168827


Let\(Y\xrightarrow{f}X\) be a morphism of compact analytic manifolds, and M a right coherentDY-module admitting a good filtration; if V⊂T*Y denotes the characteristic variety of M, one can define [M]V as the class of gr M in some suitable Grothendieck group of sheaves with support in V. Let\(T*Y\xleftarrow{F}Y\mathop { \times T*X\xrightarrow{{\bar f}}T*X}\limits_X \) be the morphisms naturally defined by f. A result of Kashiwara says that, for all i, the characteristic variety of ∫fiM is contained in\(W = \bar fF^{ - 1} V\). Here we prove the following K-theoretic version of this result:\(\sum {( - 1)^i [\int_f^i {M]} _W } = \bar f_* F*[M]_V \).

Copyright information

© Springer-Verlag 1985