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Image inverse d'un $\cal D$-module et polygone de Newton (Inverse Image of a$\cal D$-module and Newton Polygon)

Published online by Cambridge University Press:  04 December 2007

Yves Laurent  and
Zoghman Mebkhout
Yves Laurent
Affiliation:
Université de Grenoble, Institut Fourier, UMR 5584 CNRS/UJF, BP 74, 38042 St Martin d'Hères Cedex, France. E-mail: yves.laurent@ujf-grenoble.fr
Zoghman Mebkhout
Affiliation:
Université de Paris 7 UFR de Mathématiques, 175 rue de Chevaleret, 75013 Paris, France. E-mail: mebkout@math.jussieu.fr
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Abstract

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We show that, under conditions about the microcharacteristic variety of a coherent $\cal D$-module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic $\cal D$-module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.

Keywords

$\cal D$-modulesirregularityindexholonomicGevrey
Type
Research Article
Information
Compositio Mathematica , Volume 131 , Issue 1 , March 2002 , pp. 97 - 119
Copyright
© 2002 Kluwer Academic Publishers