Derived moduli of schemes and sheaves
arXiv:1011.2742
Abstract
We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks. Examples of problems represented by derived geometric 1-stacks are derived moduli of polarised projective varieties, derived moduli of vector bundles, and derived moduli of abelian varieties.
33 pages; v2 polarised abelian varieties corrected (Remark 3.46); v3 final version, to appear in JKT; v4 running typo (local -> complete local) corrected; v5 refs updated; v6 Prop 2.32 added, with consequent simplification of hypersheaf conditions in representability theorems; v7 added missing hypothesis for moduli of complexes