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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