2018/08/15 by Meazzini, Francesco
#14D15 #14F05 #16W50 #18G55 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1808.05119
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.