A Coboundary Morphism For The Grothendieck Spectral Sequence
arXiv:1112.6295 · doi:10.1007/s10485-013-9306-y
Abstract
Given an abelian category with enough injectives we show that a short exact sequence of chain complexes of objects in 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.
18 pages