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arXiv · 1808.05119

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

Francesco Meazzini
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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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Francesco Meazzini. 2018-08-15. A DG-enhancement of D(QCoh(X)) with applications in deformation theory. https://arxiv.org/abs/1808.05119

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