Homology, Homotopy and Applications
Volume 10 (2008)
The algebraic $K$-theory of a diagram of rings
Pages: 13 – 58
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. The main result of this paper is the direct comparison of the filtration in classical algebraic $K$-theory discussed in J. Duflot, “Simplicial groups that are models for algebraic $K$-theory,” Manuscripta Math. 113 (2004), no. 4, 423-470 and J. Duflot and C.T. Marak, “A filtration in algebraic $K$-theory,” J. Pure Applied Algebra 151 (2000), no. 2, 135-162 to a corresponding filtration in the Bousfield-Kan spectral sequence associated to a Tot-tower of simplicial groups attached to the diagram of rings.
algebraic $K$-theory; simplicial group
2010 Mathematics Subject Classification
18G30, 18G55, 19Dxx, 55U10