Sur L'Annulation du deuxième foncteur de (co)homologie D'André-Quillen

Abstract

For a given ideal I of a commutative ring ç A,B = A/I, the vanishing of the second André-Quillen (co)homology functor H2(A,B,*) is characterized in terms of the canonical homomorphism a:S(I)->R(I) from the symmetric algebra of the ideal I onto its Rees algebra. This is done by introducing a Koszul complex that characterizes commutative graded algebras which are symmetric algebras.