The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomology

2005/10/15 by J. C. Liu, Liu, J. C., M. W. Rogers +2
Mathematics · #13D45 (Primary) 13H10 (Secondary) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AC #msc:13D45 #msc:13H10

paper · pdf · doi:10.48550/arxiv.math/0510322

Under review. 21 pages

arxiv created 2005/10/15 · openalex publication_date 2005/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if M is a finitely-generated module of dimension d with finite local cohomologies over a Noetherian local ring, and if the ith local cohomology module of M is zero unless i = d, i = 0, and i = r for some r strictly between 0 and d, then there is an integer l such that every parameter ideal for M contained in the lth power of the maximal ideal has the same index of reducibility on M. This theorem generalizes work of the second author (math.AC/0408143) and is closely related to work of S. Goto, H. Sakurai (math.AC/0306148), and N. Suzuki.

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