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arXiv · 1801.02992

Blown-up intersection cochains and Deligne's sheaves

David Chataur·Martintxo Saralegi-Aranguren·Daniel Tanré
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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.

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David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré. 2018-01-09. Blown-up intersection cochains and Deligne's sheaves. https://doi.org/10.1007/s10711-019-00458-w

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