  We propose a generalization of a conjecture of D. Quillen, on the vanishing
of Andr\'e-Quillen homology, to simplicial commutative rings. This conjecture
characterizes a notion of local complete intersection, extended to the
simplicial setting, under a suitable hypothesis on the local characteristic.
Further, under the condition of finite-type homology, we then prove the
conjecture in the case of a simplicial commutative algebra augmented over a
field of non-zero characteristic. As a consequence, we obtain a proof of
Quillen's conjecture for a Noetherian commutative algebra - again augmented
over a field of non-zero characteristic.
