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2018-08-24

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193547

On some local cohomology spectral sequences

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https://doi.org/10.1093/imrn/rny186

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.

Subject

Àlgebra homològica, Anells commutatius, Àlgebra commutativa, Successions espectrals (Matemàtica), Topologia algebraica

Subject (English)

Homological algebra, Commutative rings, Commutative algebra, Spectral sequences (Mathematics), Algebraic topology

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

ÀLVAREZ MONTANER, Josep, FERNANDEZ BOIX, Alberto and ZARZUELA, Santiago. On some local cohomology spectral sequences. International Mathematics Research Notices. 2018. Vol. 2020, num. 19, pags. 6197-6293. ISSN 1073-7928. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/193547

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