Blown-up intersection cochains and Deligne's sheaves

TL;DR

This paper demonstrates that blown-up intersection cochains can be realized as Deligne's sheaves, connecting intersection cohomology with sheaf theory and duality in stratified spaces.

Contribution

It proves that blown-up intersection cochains correspond to Deligne's sheaves, enabling their realization as complexes of soft sheaves of perverse differential graded algebras.

Findings

Blown-up intersection cochains are realizations of Deligne's sheaves.

Establishment of Poincaré and Verdier dualities for blown-up intersection sheaves.

Connection between intersection cohomology and sheaf-theoretic frameworks.

Abstract

In a series of papers the authors introduced the so-called blown-up intersection cochains. These cochains are suitable to study products and cohomology operations of intersection cohomology of stratified spaces. The aim of this paper is to prove that the sheaf versions of the functors of blown-up intersection cochains are realizations of Deligne's sheaves. This proves that Deligne's sheaves can be incarnated at the level of complexes of sheaves by soft sheaves of perverse differential graded algebras. We also study Poincar\'e and Verdier dualities of blown-up intersections sheaves with the use of Borel-Moore chains of intersection.