Michel, Nicolas
Parametrized K-theory
Journal of K-theory
In 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.;
2013
http://infoscience.epfl.ch/record/185104/files/Michel_KTheory.pdf;