Àlvarez Montaner, JosepFernandez Boix, AlbertoZarzuela, Santiago2023-02-132023-02-132018-08-241073-7928https://hdl.handle.net/2445/193547We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set.The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by applying a family of functors to a single module. For the 2nd type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their 2nd page. As a consequence we obtain some decomposition theorems that greatly generalize the wellknown decomposition formula for local cohomology modules of Stanley-Reisner rings given by Hochster.97 p.application/pdfeng(c) Àlvarez Montaner, Josep et al., 2018Àlgebra homològicaAnells commutatiusÀlgebra commutativaSuccessions espectrals (Matemàtica)Topologia algebraicaHomological algebraCommutative ringsCommutative algebraSpectral sequences (Mathematics)Algebraic topologyinfo:eu-repo/semantics/article6822112023-02-13info:eu-repo/semantics/openAccess