  A classic result by Raynaud and Gruson says that the notion of an (infinite
dimensional) vector bundle is Zariski local. This result may be viewed as a
particular instance (for n = 0) of the locality of more general notions of
quasi-coherent sheaves related to (infinite dimensional) n-tilting modules and
classes. Here, we prove the latter locality for all n and all schemes. We also
prove that the notion of a tilting module descends along arbitrary faithfully
flat ring morphisms in several particular cases (including the case when the
base ring is noetherian).
