On the vanishing and non-rigidity of the André-Quillen (co)homology (Q1366718)

Let \(I\) be an ideal of a commutative ring \(A\) and \(B=A/I\). Given \(n\geq 2\), the author characterizes the vanishing of the André-Quillen homology modules \(H_p(A,B,w)\) for all \(B\)-modules \(w\) and for all \(p\), \(2\leq p\leq n\), in terms of canonical morphisms. His theorem is a generalization of previous characterizations given by Quillen and André for \(n=\infty\). -- When \(A\) is noetherian, it is well-known that the vanishing of the second homology functor for all modules implies the vanishing of all higher ones. In this text the author gives a commutative local ring \(A\) of Krull dimension 2 of maximal ideal \(I\) and quotient \(B=A/I\) such that for all \(B\)-modules \(W\), \(H_2 (A,B,W)=0\) and \(H_3 (A,B,W)= W\).