Stratifications of real vector spaces from constructible sheaves with conical microsupport

TL;DR

This paper proves two conjectures by Kashiwara and Schapira, establishing stratifications of real vector spaces compatible with certain constructible sheaves and their microsupports, advancing the understanding of sheaf theory in real geometry.

Contribution

It confirms conjectures on stratifications of real vector spaces aligned with microsupport conditions using derived categories of constructible sheaves.

Findings

Proves existence of compatible stratifications for sheaves with given microsupports.

Establishes a link between sheaf theory and stratification theory in real vector spaces.

Advances the theoretical framework for subanalytic sheaves and conic topology.

Abstract

Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two conjectures due to Kashiwara and Schapira concerning the existence of stratifications of real vector spaces that play well with sheaves having microsupport in a given cone or, equivalently, sheaves in the corresponding conic topology.