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On the growth of the Betti sequence of the canonical module

On the growth of the Betti sequence of the canonical module We study the growth of the Betti sequence of the canonical module of a Cohen–Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen–Macaulay ring possessing a canonical module to be Gorenstein. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

On the growth of the Betti sequence of the canonical module

Mathematische Zeitschrift , Volume 256 (3) – Jan 10, 2007

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-006-0096-x
Publisher site
See Article on Publisher Site

Abstract

We study the growth of the Betti sequence of the canonical module of a Cohen–Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen–Macaulay ring possessing a canonical module to be Gorenstein.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jan 10, 2007

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