  The use of homological and homotopical devices, such as Tor and
Andr\'e-Quillen homology, have found substantial use in characterizing
commutative algebras. The primary category setting has been differentially
graded algebras and modules, but recently simplicial categories have also
proved to be useful settings. In this paper, we take this point of view up a
notch by extending some recent uses of homological algebra in characterizing
Noetherian commutative algebras to characterizing simplicial commutative
algebras having finite Noetherian homotopy through the use of simplicial
homotopy theory. These characterizations involve extending the notions of
locally complete intersections and locally Gorenstein algebras to the
simplicial homotopy setting.
