Volume 17, issue 1 (2013)

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Deriving Deligne–Mumford stacks with perfect obstruction theories

Timo Schürg

Geometry & Topology 17 (2013) 73–92
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