We establish a comparison between the notion of derived Deligne–Mumford stack in
the sense of Toën and Vezzosi and the one introduced by Lurie. 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 it sometimes being useful to be able to switch
between the two frameworks.
Keywords
derived stack, Deligne–Mumford stack, spectral stack, HAG
II, DAG V