A DG-enhancement of D(QCoh(X)) with applications in deformation theory

Abstract

It is well-known that DG-enhancements of D(QCoh(X)) are all equivalent to each other, see [23]. Here we present an explicit model which leads to applications in deformation theory. In particular, we shall describe three models for derived endomorphisms of a quasi-coherent sheaf F on a finite-dimensional Noetherian separated scheme (even if F does not admit a locally free resolution). Moreover, these complexes are endowed with DG-Lie algebra structures, which we prove to control infinitesimal deformations of F.

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• Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves
• Cohomology of partially ordered sets and local cohomology of section rings
• Mirrors, Functoriality, and Derived Geometry
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Cited by in corpus (4)

• Formality conjecture for minimal surfaces of Kodaira dimension 0
• Deformations of algebraic schemes via Reedy-Palamodov cofibrant resolutions
• Connections and $L_{\infty }$ liftings of semiregularity maps
• Endomorphisms of Koszul complexes: formality and application to deformation theory