Derived moduli of schemes and sheaves

J.P. Pridham
2011 Journal of K-Theory  
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. The author was supported during this research by the Engineering and Physical Sciences Research Council
more » ... nt number EP/F043570/1]. of abelian schemes (Example 3.45) and derived Hom-stacks (Example 3.37). Section 4 deals, in Theorem 4.12 and Example 4.15, with moduli of quasi-coherent complexes. Lemma 4.16 then checks that the paper's two possible approaches to derived moduli of vector bundles (via GL n -torsors and via quasi-coherent complexes) give equivalent results, which was already known in the framework of [TV2] .
doi:10.1017/is011011012jkt175 fatcat:zjkboyfzq5dfxpmsqckcbsxnka