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The index of reducibility of parameter ideals in low dimension

Mark W. Rogers
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Abstract

Results are presented concerning the following question: If M is a finitely-generated module with finite local cohomologies over a Noetherian local ring (A, m), does there exist an integer n such that every parameter ideal for M contained in m^n has the same index of reducibility? We show that the answer is yes if M has dimension 1 or if M has dimension 2 and positive depth. This research is closely related to work of Goto-Suzuki and Goto-Sakurai; Goto-Sakurai have supplied an answer of yes in case M is Buchsbaum.

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Mark W. Rogers. 2004-08-11. The index of reducibility of parameter ideals in low dimension. https://arxiv.org/abs/math/0408143

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