On simplicial commutative algebras with finite Andre-Quillen homology

by James M. Turner

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.  Note: this paper replaces
"Nilpotency in the homotopy of simplicial commutative algebras".