Geodesic
The algebraic $K$-theory of a diagram of rings
Homology, homotopy, and applications, Tome 10 (2008) no. 2, pp. 13-58.

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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.
DOI : 10.4310/HHA.2008.v10.n2.a2
Classification : 18G30, 18G55, 19Dxx, 55U10
Keywords: algebraic $K$-theory, simplicial group 
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Jeanne Duflot. The algebraic $K$-theory of a diagram of rings. Homology, homotopy, and applications, Tome 10 (2008) no. 2, pp. 13-58. doi : 10.4310/HHA.2008.v10.n2.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n2.a2/

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