Translator Disclaimer
November 2019 Generalizations of Intersection Homology and Perverse Sheaves with Duality over the Integers
Greg Friedman
Michigan Math. J. 68(4): 675-726 (November 2019). DOI: 10.1307/mmj/1564711315

Abstract

We provide a generalization of the Deligne sheaf construction of intersection homology theory and a corresponding generalization of Poincaré duality on pseudomanifolds such that the Goresky–MacPherson, Goresky–Siegel, and Cappell–Shaneson duality theorems all arise as particular cases. Unlike classical intersection homology theory, our duality theorem holds with ground coefficients in an arbitrary PID and with no local cohomology conditions on the underlying space. Self-duality does require local conditions, but our perspective leads to a new class of spaces more general than the Goresky–Siegel IP spaces on which upper-middle perversity intersection homology is self-dual. We also examine torsion-sensitive t-structures and categories of perverse sheaves that contain our torsion-sensitive Deligne sheaves as intermediate extensions.

Citation

Download Citation

Greg Friedman. "Generalizations of Intersection Homology and Perverse Sheaves with Duality over the Integers." Michigan Math. J. 68 (4) 675 - 726, November 2019. https://doi.org/10.1307/mmj/1564711315

Information

Received: 27 December 2016; Revised: 14 May 2019; Published: November 2019
First available in Project Euclid: 2 August 2019

zbMATH: 07155045
MathSciNet: MR4029625
Digital Object Identifier: 10.1307/mmj/1564711315

Subjects:
Primary: 55M05, 55N30, 55N33, 57N80

Rights: Copyright © 2019 The University of Michigan

JOURNAL ARTICLE
52 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.68 • No. 4 • November 2019
Back to Top