Some spectral sequences for filtered complexes and applications
type: Item
instance of: scholarly article
title: Some spectral sequences for filtered complexes and applications
zbMATH Open document ID: 0876.18007
published in: Journal of Algebra
publication date: 1997-10-28T00:00:00Z
review text: Let \(f: {\mathcal A}\to {\mathcal A}'\) be a left exact functor between abelian categories, such that \(\mathcal A\) has enough injectives, and let \(C\in \mathcal A\) be a filtered complex. A series of spectral sequences converging to the derived functors of \(f\) applied to \(C\) are obtained as the derived functors of \(f\) applied to the complexes given by Deligne's shift procedure. As an application, the author obtains a Leray spectral sequence for the de Rham cohomology and a comparison with the Leray spectral sequence for singular cohomology, as well as a comparison between Bloch-Ogus coniveau spectral sequences and Leray spectral sequences induced by the canonical map from a site which is finer than the Zariski site.
Mathematics Subject Classification ID: 18G40
Mathematics Subject Classification ID: 18E25
Mathematics Subject Classification ID: 18G35
Mathematics Subject Classification ID: 19E20
Mathematics Subject Classification ID: 14F40
zbMATH DE Number: 1013953
zbMATH Keywords: abelian categories
zbMATH Keywords: filtered complex
zbMATH Keywords: derived functors
zbMATH Keywords: Deligne's shift procedure
zbMATH Keywords: Leray spectral sequence
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: singular cohomology
zbMATH Keywords: Bloch-Ogus coniveau spectral sequences
zbMATH Keywords: Zariski site
author: Kapil H. Paranjape
reviewed by: Luca Barbieri-Viale
MaRDI profile type: Publication
full work available at URL: jabr.1996.0395
OpenAlex ID: W2033671250
DOI: 10.1006/JABR.1996.0395
description: scientific article; zbMATH DE number 1013953