On a theorem of Gulliksen on ideals of finite projective dimension

Abstract

We show that a modification of the proof of a result of Gulliksen gives an elementary proof of the following important theorem by Avramov: if f:(A,m,k)→(B,n,l) is a homomorphism of noetherian local rings and B is of finite flat dimension over A, then the homomorphism induced in André-Quillen homology modules H2(A,l,l)→H2(B,l,l) is injective.