  L. Avramov, following D. Quillen, posed a conjecture to the effect that if $R
\to A$ is a homomorphism of Noetherian rings then the Andr\'e-Quillen homology
on the category of A-modules satisfies: $D_{s}(A|R;-) = 0$ for $s\gg 0$ implies
$D_{s}(A|R;-) = 0$ for s>2. In an earlier paper, the author posed an extended
version of this conjecture which considered A to be a simplicial commutative
R-algebra with Noetherian homotopy such that the characteristic of $\pi_{0}A$
is non-zero. In addition, a homotopy characterization of such algebras was
described. The main goal of this paper is to develop a strategy for
establishing this extended conjecture and provide a complete proof when R is
Cohen-Macaulay of characteristic 2.
