Showing papers on "Ringed space published in 2008"
TL;DR: In this article, it was shown that the deformations of the abelian category Mod(O) of sheaves of O-modules are obtained from algebroid prestacks, as introduced by Kontsevich.
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).
24 citations
TL;DR: The category of formal geometries is defined, a natural abstraction from that of locally ringed spaces, which allows the author to eventually phrase and prove, still within the language of opens and sections, the universal property of the Zariski spectrum.
12 citations