The quantum site of a schematic algebra

Abstract

The class of schematic algebras consists of algebras possessing “enough” Ore-sets (cfr. [14]) and is reasonably large (cfr. [15]). To a schematic algebra, we associate a generalised Grothendieck topology such that Serre’s Theorem holds, i.e. Artin’s Proj (cfr. [1]) is equiv-alent to the category of coherent sheaves. In this paper we construct a genuine Grothendieck topology for a schematic algebra. The price we have to pay is that the sections of a coherent sheaf are quantum sections of a module instead of Ore-localisations.