j -Filtrations

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 I. The general notion of pre- j -filtration is introduced as a convenient abelian category to work in. The notion of j -filtration is first considered when the talé space of is Hausdorff. We will soon restrict to j -filtrations of locally constant sheaves of k-vector spaces and we will extend the definition to the case where 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.