On the growth of the Betti sequence of the canonical module |
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Authors: | David A Jorgensen Graham J Leuschke |
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Institution: | (1) Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA;(2) Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, USA |
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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.
GJL was partly supported by a grant from the National Security Agency.
An erratum to this article can be found at |
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