Algebroid prestacks and deformations of ringed spaces

Abstract

For a ringed space (X,O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules (Lowen and Van den Bergh, 2006) are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasi-compact separated scheme the same is true for Qch(O), the category of quasi-coherent sheaves on X. It follows in particular that there is a deformation equivalence between Mod(O) and Qch(O).