Michel, Nicolas2013-03-192013-03-192013-03-192013https://infoscience.epfl.ch/handle/20.500.14299/904731304.0520In nature, one observes that a K-theory of an object is defined in two steps. First a “structured” category is associated to the object. Second, a K-theory machine is applied to the latter category that produces an infinite loop space. We develop a general framework that deals with the first step of this process. The K-theory of an object is defined via a category of “locally trivial” objects with respect to a pretopology. We study conditions ensuring an exact structure on such categories. We also consider morphisms in K-theory that such contexts naturally provide. We end by defining various K-theories of schemes and morphisms between them.K-theory – Local triviality – Exact categories – Monoidal fibred categories – Fibred Grothendieck sites – Modules – Sheaves of modules.text::preprint