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Applied Categorical Structures

, Volume 22, Issue 1, pp 269–288 | Cite as

A Coboundary Morphism for the Grothendieck Spectral Sequence

  • David Baraglia
Article

Abstract

Given an abelian category \(\mathcal{A}\) with enough injectives we show that a short exact sequence of chain complexes of objects in \(\mathcal{A}\) gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.

Keywords

Spectral sequence Grothendieck Leray Coboundary Filtration 

Mathematics Subject Classifications (2010)

18G40 18G10 55Txx 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesThe University of AdelaideAdelaideAustralia

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