Deriving Deligne-Mumford Stacks with Perfect Obstruction Theories

Abstract

We give conditions for a n-connective quasicoherent obstruction theory on a Deligne-Mumford stack to come from the structure of a connective spectral Deligne-Mumford stack on the underlying topos.

25 pages; v.4: Assumptions added to correct Lemma; Main result now gives necessary and sufficient conditions for an obstruction theory to be induced by a derived structure; Erratum to published version is to appear

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