On some local cohomology spectral sequences
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We 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 well-known decomposition formula for local cohomology modules of Stanley–Reisner rings given by Hochster.
CitacióAlvarez, J.; Boix, A.; Zarzuela, S. On some local cohomology spectral sequences. "International mathematics research notices", 2020, vol. 2020, núm. 19, p. 6197-6293.