Sobre sequências espectrais

Abstract

Spectral sequence is a tool used to calculate, via sucessing aproximations, the homologies of a chain complex; is employed whenever have a ?ltration of the cocmplex and we can not calculate its homologies directly. Each ?ltration of a chain complex gives rise to a spectral sequence and, depending on the properties of the ?ltration, we obtain properties of the homology of the complex. In this work are presented, under the bias of Category Theory, concepts and basic results of Homological Algebra, such as the long exact sequence theorem, resolutions and d-functors (derived functors). Next we deal with the algebraic theory of spectral sequences, apply it in bicomplexes and speak in hyperhomology, ending with the Grothendieck’ spectral sequence and applications in the theory of modules.