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2008 The algebraic $K$-theory of a diagram of rings
Jeanne Duflot
Homology Homotopy Appl. 10(2): 13-58 (2008).


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.


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Jeanne Duflot. "The algebraic $K$-theory of a diagram of rings." Homology Homotopy Appl. 10 (2) 13 - 58, 2008.


Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1145.19003
MathSciNet: MR2426128

Primary: 18G30 , 18G55 , 19D99 , 55U10

Keywords: algebraic $K$-theory , simplicial group

Rights: Copyright © 2008 International Press of Boston


Vol.10 • No. 2 • 2008
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