  In this article we fix a prime integer $p$ and compare certain dg algebra
resolutions over a local ring whose residue field has characteristic $p$.
Namely, we show that given a closed surjective map between such algebras there
is a precise description for the minimal model in terms of the acyclic closure,
and that the latter is a quotient of the former. A first application is that
the homotopy Lie algebra of a closed surjective map with residual
characteristic $p$ is abelian. We also use these calculations to show
deviations enjoy rigidity properties which detect the (quasi-)complete
intersection property.
