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October 20, 2025Open Access

Koszul cohomology and support of local cohomology modules of complete intersections

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Support of local cohomology modules is shown to be Zariski-closed in regular noetherian rings.
Koszul cohomology connects the local cohomology of complete intersections indicating deeper algebraic properties.
A framework introduced to analyze the support of local cohomology with respect to regular sequences.
Application of the main findings demonstrates significant results for ideals in noetherian regular rings.

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Research shows that the support of local cohomology modules is Zariski-closed in regular rings, suggesting new avenues in algebraic geometry.

Gintz et al. (2025) studied this question.

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Research shows that the support of local cohomology modules is Zariski-closed in regular rings, suggesting new avenues in algebraic geometry.