Bass numbers and Massey products. (Q1181455)

Let \((R,m)\) be a local commutative noetherian ring. The first Bass numbers \(\mu_ i\) depend only on the algebra structure of the homology of the Koszul complex \(K\) of \((R,m)\). More precisely, denoting by \(d\) the depth of \(R\), we have: \(\mu_ d=\text{dimension}(H_{n-d}(K))\), \(\mu_{d+1}=\{x\in H_ *(k)\hbox{ s.t. }x \cdot H_ 1(K)=0\}\). \(\mu_{d+2}\) and \(\mu_{d+3}\) are also determined in terms of the multiplication law and the Massey products of \(H_ *(K)\). To prove the theorems, the author uses the DG algebras methods initiated by Avramov, Foxby and Lescot.