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arXiv · 1802.02025

On some local cohomology spectral sequences

Josep Àlvarez Montaner·Alberto F. Boix·Santiago Zarzuela
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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.

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Josep Àlvarez Montaner, Alberto F. Boix, Santiago Zarzuela. 2018-07-17. On some local cohomology spectral sequences. https://doi.org/10.1093/imrn%2Frny186

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