Rings that are Homologically of Minimal Multiplicity

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 R i (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.

Applications of Differential Graded Algebra Techniques in Commutative Algebra

“…Christensen, Striuli, and Veliche [45] conduct a careful analysis of several special cases of this and other related questions. Other progress comes from Jorgensen and Leuschke [75] and Borna, Sather-Wagstaff, and Yassemi [33,105].…”