On some local cohomology spectral sequences

Abstract

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 first type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain applying a family of functors to a single module. For the second 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 second page. As a consequence we obtain some decomposition theorems that greatly generalize the well-known decomposition formula for local cohomology modules given by Hochster.

63 pages, comments are welcome. To appear in International Mathematics Research Notices

References in corpus (9)

• Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals
• Cohomology of partially ordered sets and local cohomology of section rings
• On toric face rings
• Regularity and cohomology of determinantal thickenings
• On algebras associated to partially ordered sets
• Gröbner bases and Betti numbers of monoidal complexes
• Seminormality and local cohomology of toric face rings
• Injective modules over some rings of Differential operators
• Local Picard Group of Binoids and Their Algebras