K-Theory of Truncated Polynomial Algebras

Lars Hesselholt ()
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Lars Hesselholt: Massachusetts Institute of Technology, Department of Mathematics

Chapter I.3 in Handbook of K-Theory, 2005, pp 71-110 from Springer

Abstract: Abstract In general, if A is a ring and I ⊂ A a two-sided ideal, one defines the K-theory of A relative to I to be the mapping fiber of the map of K-theory spectra induced by the canonical projection from A to A/I. Hence, there is anatural exact triangle of spectra $$ K(A,I) \rightarrow K(A) \rightarrow K(A/I) \xrightarrow{\partial} K(A,I)[-1] $$ and an induced natural long-exact sequence of K-groups $$ ... \rightarrow K_{q}(A,I) \rightarrow K_{q}(A) \rightarrow K_{q}(A/I) \xrightarrow{\partial} K_{q-1}(A,I) \rightarrow ... $$ .

Keywords: Homotopy Group; Geometric Realization; Cyclic Homology; Smash Product; Symmetric Monoidal Category (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/978-3-540-27855-9_3

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