This research explores Koszul cohomology linked to local cohomology in Noetherian rings, suggesting implications for Zariski-closed properties.
Let be a Noetherian commutative ring and be a regular sequence in . We introduce a framework to study by linking the Koszul cohomology of on the sequence and local cohomology modules . As an application, we prove that if is a Noetherian regular ring of prime characteristic and form a regular sequence, then is Zariski‐closed for each integer and each ideal .
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Gintz et al. (2026) studied this question.
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