Ultrafunctor

Abstract

Let G be a functor from commutative rings to abelian groups and let ﹛Rt : i ∈ S﹜ be a family of commutative rings indexed by the set S. Let be an ultrafilter on S, and let denote the ultraproduct of the Rt with respect to . This paper studies the problem of computing from the G(Rj) via the mapThe functors studied are Pic = Picard group, Br = Brauer group, U = units, and the functors K0, K1, SK1, K2 of Algebraic K-Theory. For G = Pic, U, K1 and SK1, (*) is always a monomorphism. An example is given to show that even if all the Rt are finite fields the map (*) has a kernel for G = K2.