  The Ziegler spectrum for categories enriched in closed symmetric monoidal
Grothendieck categories is defined and studied in this paper. It recovers the
classical Ziegler spectrum of a ring. As an application, the Ziegler spectrum
as well as the category of generalised quasi-coherent sheaves of a reasonable
scheme is introduced and studied. It is shown that there is a closed embedding
of the injective spectrum of a coherent scheme endowed with the tensor
fl-topology (respectively of a noetherian scheme endowed with the dual Zariski
topology) into its Ziegler spectrum. It is also shown that quasi-coherent
sheaves and generalised quasi-coherent sheaves are related to each other by a
recollement.
