  In this paper, we study the Andr\'e-Quillen homology of simplicial
commutative $\ell$-algebras, $\ell$ a field, having certain vanishing
properties. When $\ell$ has non-zero characteristic, we obtain an algebraic
version of a theorem of J.-P. Serre and Y. Umeda that characterizes such
simplicial algebras having bounded homotopy groups. We further discuss how this
theorem fails in the rational case and, as an application, indicate how the
algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for
algebras of finite type over Noetherian rings, which have non-zero
characteristic.
