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http://hdl.handle.net/2445/193547
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: https://doi.org/10.1093/imrn/rny186 |
It is part of: | International Mathematics Research Notices, 2018, vol. 2020, num. 19, p. 6197-6293 |
URI: | http://hdl.handle.net/2445/193547 |
Related resource: | https://doi.org/10.1093/imrn/rny186 |
ISSN: | 1073-7928 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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