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

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

2005-10-15

arxiv.org/abs/math/0510322v1

Mathematics

Commutative Algebra

Under review. 21 pages

Scientific paper

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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