Comparison results for derived Deligne-Mumford stacks

Abstract

In this short note we write down a comparison between the notion of derived Deligne-Mumford stack in the sense of B. To\"en and G. Vezzosi [HAG-II] and the one introduced by J. Lurie in [DAG-V]. It is folklore that the two theories yield essentially the same objects, but it is difficult to locate in the literature a precise result, despite being sometimes useful to be able to switch between the two frameworks.