Blown-up intersection cochains and Deligne's sheaves
Algebraic Topology
2020-09-22 v2
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.
Keywords
Cite
@article{arxiv.1801.02992,
title = {Blown-up intersection cochains and Deligne's sheaves},
author = {David Chataur and Martintxo Saralegi-Aranguren and Daniel Tanré},
journal= {arXiv preprint arXiv:1801.02992},
year = {2020}
}