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Sur les Images Directes deD-Modules

Authors:	Bernard Malgrange

Institution:	(1) Institut Fourier, Université de Grenoble I, B.P. 74, 38402 Saint-Martin-d1 Hères Cedex, France

Abstract:	Let $Y\xrightarrow{f}X$ be a morphism of compact analytic manifolds, and M a right coherentD _Y-module admitting a good filtration; if VTY 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 $TY\xleftarrow{F}Y\mathop { \times TX\xrightarrow{{\bar f}}TX}\limits_X$ be the morphisms naturally defined by f. A result of Kashiwara says that, for all i, the characteristic variety of _f ⁱ M is contained in $W = \bar fF^{ - 1} V$ . Here we prove the following K-theoretic version of this result: $\sum {( - 1)^i \int_f^i {M]} _W } = \bar f_* F*M]_V$ . C'est un grand plaisir pour moi de publier cet article dans ce volume, et de l'offrir en hommage à Monsieur K. Stein

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