On simplicial commutative algebras with vanishing Andre-Quillen homology

In this paper, we study the Andre-Quillen homology of simplicial commutativ e l-algebras, l a field, having certain vanishing properties. When l has no n-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having boun ded homotopy groups. We further discuss how this theorem fails in the ratio nal case and, as an application, indicate how the algebraic Serre theorem c an be used to resolve a conjecture of D. Quillen for algebras of finite typ e over Noetherian rings, having non-zero characteristic.