  In this article we use our constructions from "Enlargements of Categories"
(Theory and Applications of Categories, 14:357-398) to lay down some
foundations for the application of A. Robinson's nonstandard methods to modern
Algebraic Geometry. The main motivation is the search for another tool to
transfer results from characteristic zero to positive characteristic and vice
versa. We give applications to the resolution of singularities and weak
factorization.
