The algebraic $K$-theory of a diagram of rings

Abstract

In this paper, we consider "diagrams of rings", or functors from a small category to the category of rings, and the corresponding diagrams of groups K i . Classically, this was initiated by Milnor [13]. The main result of this paper is the direct comparison of the filtration in classical algebraic K-theory discussed in [6,7] to a corresponding filtration in the BousfieldKan spectral sequence associated to a Tot-tower of simplicial groups attached to the diagram of rings.