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On the growth of the Betti sequence of the canonical module

David A. Jorgensen·Graham J. Leuschke
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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.

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David A. Jorgensen, Graham J. Leuschke. 2006-04-03. On the growth of the Betti sequence of the canonical module. https://arxiv.org/abs/math/0603693

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