A Coboundary Morphism for the Grothendieck Spectral Sequence

作者：Baraglia David^*

来源：Applied Categorical Structures, 2014, 22(1): 269-288.

DOI：10.1007/s10485-013-9306-y

• Spectral sequence
• Grothendieck
• Leray
• Coboundary
• Filtration

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.

• 出版日期2014-2