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.
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This work is supported by the Australian Research Council Discovery Project DP110103745.
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Baraglia, D. A Coboundary Morphism for the Grothendieck Spectral Sequence. Appl Categor Struct 22, 269–288 (2014). https://doi.org/10.1007/s10485-013-9306-y
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DOI: https://doi.org/10.1007/s10485-013-9306-y