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arXiv · 1112.6295

A Coboundary Morphism For The Grothendieck Spectral Sequence

David Baraglia
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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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David Baraglia. 2011-12-29. A Coboundary Morphism For The Grothendieck Spectral Sequence. https://doi.org/10.1007/s10485-013-9306-y

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