Sheaves for analysis: an overview (Microlocal Analysis and Singular Perturbation Theory)

Abstract

This is an expository paper, without proofs, extracted from the paper [GS16] with Stéphane Guillermou. We show how the use of Grothendieck topologies on a real analytic manifold allows one to recover classical spaces of analysis which are not of local nature for the usual topology. We apply these results to endow the subanalytic sheaf of holomorphic functions with a filtration, then to endow regular holonomic D-modules with a functorial filtration (in the derived sense).