About a variation of local cohomology
M. Azeem Khadam, Peter Schenzel

TL;DR
This paper explores a variation of local cohomology by examining specific subcomplexes of the Čech complex, establishing properties like Artinianness for certain cohomology modules and characterizing their last non-vanishing degree.
Contribution
It introduces a new approach to approximate local cohomology modules using subcomplexes of the Čech complex and proves their Artinianness in the case of -primary ideals.
Findings
Cohomology modules approximate local cohomology modules.
Proved Artinianness of these modules for -primary ideals.
Characterized the last non-vanishing cohomology module.
Abstract
Let denote an ideal of a local ring . For a system of elements such that and we investigate a subcomplex resp. a factor complex of the \v{C}ech complex for a finitely generated -module . We start with the inspection of these cohomology modules that approximate in a certain sense the local cohomology modules for all . In the case of an -primary ideal we prove the Artinianness of these cohomology modules and characterize the last non-vanishing among them.
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