Details

Autor(en) / Beteiligte

• Àlvarez Montaner, Josep
• Boix, Alberto F
• Zarzuela, Santiago

Titel

On Some Local Cohomology Spectral Sequences

Ist Teil von

• International mathematics research notices, 2020-10, Vol.2020 (19), p.6197-6293

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 well-known decomposition formula for local cohomology modules of Stanley–Reisner rings given by Hochster.