Deriving Deligne–Mumford stacks with perfect obstruction theories

Schürg, Timo

doi:10.2140/gt.2013.17.73

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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

Volume 17, issue 1 (2013)