Blown-up intersection cochains and Deligne’s sheaves

被引:0
作者
David Chataur
Martintxo Saralegi-Aranguren
Daniel Tanré
机构
[1] Université de Picardie Jules Verne,Lamfa
[2] Université d’Artois,Laboratoire de Mathématiques de Lens, EA 2462
[3] Université de Lille,Département de Mathématiques, UMR 8524
来源
Geometriae Dedicata | 2020年 / 204卷
关键词
Intersection homology; Deligne sheaf; Verdier duality; Poincaré duality; Blown-up cohomology; 55N33; 14F05; 14F43; 55M05; 57P10; 55U30;
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摘要
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 Poincaré and Verdier dualities of blown-up intersections sheaves with the use of Borel–Moore chains of intersection.
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页码:315 / 337
页数:22
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