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Title: On some local cohomology spectral sequences
Author: Àlvarez Montaner, Josep
Fernandez Boix, Alberto
Zarzuela, Santiago
Keywords: Àlgebra homològica
Anells commutatius
Àlgebra commutativa
Successions espectrals (Matemàtica)
Topologia algebraica
Homological algebra
Commutative rings
Commutative algebra
Spectral sequences (Mathematics)
Algebraic topology
Issue Date: 24-Aug-2018
Publisher: Oxford University Press
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 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.
Note: Versió postprint del document publicat a:
It is part of: International Mathematics Research Notices, 2018, vol. 2020, num. 19, p. 6197-6293
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ISSN: 1073-7928
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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