Abstract
AbstractIt is well-known that DG-enhancements of the unbounded derived category $${\text {D}}_{qc}(X)$$
D
qc
(
X
)
of quasi-coherent sheaves on a scheme X are all equivalent to each other. 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 $$\mathcal {F}$$
F
on a finite-dimensional Noetherian separated scheme (even if $$\mathcal {F}$$
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 $$\mathcal {F}$$
F
.
Funder
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
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