  We classify the prelocalizing subcategories of the category of quasi-coherent
sheaves on a locally noetherian scheme. In order to give the classification, we
introduce the notion of a local filter of subobjects of the structure sheaf.
The essential part of the argument is given as results on a Grothendieck
category with certain properties. We also classify the localizing
subcategories, the closed subcategories, and the bilocalizing subcategories in
terms of filters.
