\(\mathcal{I}\)-Filtrations

  • Claude Sabbah
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2060)

Abstract

This chapter introduces the general framework for the study of the Stokes phenomenon in a sheaf-theoretic way. The underlying topological spaces are étalé spaces of sheaves of ordered abelian groups \(\mathcal{I}\). The general notion of pre-\(\mathcal{I}\)-filtration is introduced as a convenient abelian category to work in. The notion of \(\mathcal{I}\)-filtration is first considered when the talé space of \(\mathcal{I}\) is Hausdorff. We will soon restrict to \(\mathcal{I}\)-filtrations of locally constant sheaves of k-vector spaces and we will extend the definition to the case where \(\mathcal{I}\) satisfies the stratified Hausdorff property. Most of the notions introduced in this chapter will be taken up as a more concrete approach to Stokes filtrations in Chap. 2, and this chapter may be skipped in a first reading. It contains nevertheless many guiding principles for Chaps. 2, 3 and 9.

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Authors and Affiliations

  • Claude Sabbah
    • 1
  1. 1.CNRS École polytechniqueCentre de mathématiques Laurent SchwartzPalaiseauFrance

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