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Deriving Deligne–Mumford stacks with perfect obstruction theories

Timo Schürg
Geometry & Topology 17 (2013) 73–92
DOI: 10.2140/gt.2013.17.73
Abstract

We show that every n–connective quasi-coherent obstruction theory on a Deligne–Mumford stack comes from the structure of a connective spectral Deligne–Mumford stack on the underlying topos. Working over a base ring containing the rationals, we obtain the corresponding result for derived Deligne–Mumford stacks.

Keywords
perfect obstruction theory, derived moduli space
Mathematical Subject Classification 2010
Primary: 14A20, 18G55
Secondary: 55P43
References
Publication
Received: 22 March 2012
Revised: 7 June 2012
Accepted: 8 September 2012
Published: 17 February 2013
Proposed: Lothar Göttsche
Seconded: Richard Thomas, Jim Bryan
Authors
Timo Schürg
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
D-53115 Bonn
Germany