The purpose of this report is to introduce a formalism to produce two collections of spectral sequences. On one hand, a collection is made up by spectral sequences which involve in their second page the left derived functors of the colimit on a certain finite poset. On the other hand, the other is made up by spectral sequences which involve in their second page the right derived functors of the limit on a certain finite poset. In both cases, we provide sufficient conditions to ensure their degeneration at the second page. Finally, we see how to use our second collection of spectral sequences to produce a decomposition of local cohomology modules which can be regarded as a generalization of the classical Hochster formula for the local cohomology of a Stanley–Reisner ring.

中文翻译：

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关于一些局部上同调谱序列

本报告的目的是介绍一种生成两个光谱序列集合的形式。一方面，一个集合由谱序列组成，这些谱序列在它们的第二页中涉及某个有限偏序集上的共极限的左派生函子。另一方面，另一个由谱序列组成，在它们的第二页中涉及某个有限偏序集的极限的右派生函子。在这两种情况下，我们都提供了足够的条件来确保它们在第二页的退化。最后，我们将看到如何使用我们的第二个谱序列集合来生成局部上同调模块的分解，这可以被视为 Stanley-Reisner 环局部上同调的经典 Hochster 公式的推广。