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

[摘要] Let I be an ideal of a commutative ring A and B = A/I. Given n greater than or equal to 2, we characterize the vanishing of the Andre-Quillen homology modules H-p(A, B, W) for all B-modules W and for all p, 2 less than or equal to p less than or equal to n, in terms of some canonical morphisms. As a corollary, we obtain a new proof of a theorem of Andre. Finally, we construct an example of an ideal I of a commutative ring A such that H-2(A, B, W) = 0 and H-3(A, B, W) = W for all B-module W. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-07-21