# name
On some local cohomology spectral sequences

# metadata.dc.description.abstract[].value
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 wellknown decomposition formula for local cohomology modules of Stanley-Reisner rings given by Hochster.

# metadata.dc.relation.ispartof[].value
International Mathematics Research Notices, 2018, vol. 2020, num. 19, p. 6197-6293

# metadata.dc.rights[].value
(c) Àlvarez Montaner, Josep et al., 2018

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On some local cohomology spectral sequences