Connections between reduced Bass numbers and Auslander's \(\delta\)-invariant (Q1582752)

Let \((A, \mathfrak m)\) be a Noetherian local ring and \(M\) an \(A\)-module. The \(i\)-th Bass number of \(M\) is the length of the image of the natural homomorphism \[ \text{Ext}_A^i(A/\mathfrak m, M) \to H_{\mathfrak m}^i(M). \] It plays a key role in the theory of ``canonical element conjecture''. The authors study the relation between reduced Bass numbers and Auslander-Buchweitz's \(\delta\)-invariants. They also give a brief proof of the fact that the canonical element conjecture implies the monomial conjecture.