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arXiv · 2607.08995

$S_r$ properties of generalized Cohen--Macaulay modules and rings having liftable local cohomology via Serre depth

Haocheng Cai
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Abstract

We study Serre depth via Matlis duals of local cohomology modules. We relate the Serre depth of a module to that of a quotient by a regular element, characterize the $S_r$ property for generalized Cohen--Macaulay modules in terms of ordinary depth, and show that the $S_r$ property descends to reduced structures under liftable local cohomology hypotheses.

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Haocheng Cai. 2026-07-09. $S_r$ properties of generalized Cohen--Macaulay modules and rings having liftable local cohomology via Serre depth. https://arxiv.org/abs/2607.08995

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