Let R be a local ring and A a connected differential graded algebra over R which is free as a graded R-module. Using homological perturbation theory techniques, we construct a minimal free multi-model for $A$ having properties similar to those of an ordinary minimal model over a field; in particular the model is unique up to isomorphism of multialgebras. The attribute `multi' refers to the category of multicomplexes.
Models for differential graded algebras, minimal models for differential graded algebras over local rings, multicomplex, multialgebra, homological perturbations.
MSC 2000: 18G10, 18G35, 18G55, 55P35, 55P62, 55U15, 57T30