Vol. 287, No. 1, 2017

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ISSN: 0030-8730
Comparison results for derived Deligne–Mumford stacks

Mauro Porta

Vol. 287 (2017), No. 1, 177–197
Abstract

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
Mathematical Subject Classification 2010
Primary: 14A20
Milestones
Received: 29 March 2016
Revised: 29 July 2016
Accepted: 3 August 2016
Published: 6 February 2017
Authors
Mauro Porta
Laboratory David Rittenhouse
University of Pennsylvania
209 South 33rd Street
Philadelphia, PA 19104
United States