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2 results

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

  • Yves Laurent, Zoghman Mebkhout
  • Journal:
    Compositio Mathematica / Volume 131 / Issue 1 / March 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 97-119
    Print publication:
    March 2002
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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.

  • Formal and Tempered Solutions of Regular $\cal D$-Modules

  • Teresa Monteiro Fernandes
  • Journal:
    Compositio Mathematica / Volume 128 / Issue 3 / September 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 241-259
    Print publication:
    September 2001
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  • A new family of sheaves has been recently studied by M. Kashiwara and P. Schapira generalizing to constructible sheaves the notion of moderate and formal cohomology. We prove comparison theorems when we regard these sheaves as solutions of a $\cal D$-module. These results are natural generalizations of those of Y. Laurent and the author.