Homotopy theory of dg categories via localizing pairs and Drinfeld's DG quotient

Using localizing pairs and Drinfeld’s dg quotient we constructa new Quillen model for the homotopy theory of dg categories.We prove that, in contrast with the original model, thisnew Quillen model carries a natural closed symmetric monoidalstructure. As an application, we obtain a simple constructionof the internal Hom-objects and a conceptual characterizationof To¨en’s previous work. Making use of this new Quillen model,Lowen has recently developed a derived deformation theory.