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A Brief Glimpse of Algebraic K-theory

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Part of the Progress in Mathematics book series (PM, volume 273)

Abstract

The contents of this chapter began life as a short postgraduate course on the K-theory of Banach algebras given at the University of Southampton early in 2003. It seems appropriate for inclusion here because of the application to algebraic K-theory given in Chapter 3 § 3.3.3 which uses the rigidity results of Andrei Suslin given in [264] and [265]. In addition to a sketch of the proof of the rigidity results we shall sketch the construction of the algebraic K-theory (and K-theory mod n) for rings (that is, affine schemes — see § 4.3.1). The extension of algebraic K-theory to schemes in general is described in detail in many sources (for example [226], [227], [83], [130]) and Suslin’s results are described in a less dilettante manner in ([264], [265]; see also [142]).

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© Birkhäuser Verlag AG 2009

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