Relatively Noetherian rings, localization and sheaves. II: Structure sheaves

In the first part of this note, we have introduced a version of the (strong) second layer condition for ringsR which are relatively Noetherian with respect to some radical inR-mod and studied its impact on classical and symmetric localization theory. As an application, we now show how the relative version of the strong second layer condition allows us to endowK(), the generically closed subset of Spec(R) canonically associated to , with structure sheaves, which generalize most previously studied sheaf constructions in noncommutative algebra.