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arXiv · 0904.3982

Rings that are homologically of minimal multiplicity

Keivan Borna·Sean Sather-Wagstaff·Siamak Yassemi
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Abstract

Let R be a local Cohen-Macaulay ring with canonical module ω_R. We investigate the following question of Huneke: If the sequence of Betti numbers \{β_i^R(ω_R)\} has polynomial growth, must R be Gorenstein? This question is well-understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide several characterizations of the rings in this class and establish a general ascent and descent result.

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Keivan Borna, Sean Sather-Wagstaff, Siamak Yassemi. 2010-01-12. Rings that are homologically of minimal multiplicity. https://arxiv.org/abs/0904.3982

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