## Topological K-theory of Algebraic K-theory Spectra (1999)

Venue: | J. Algebraic K-Theory |

Citations: | 10 - 3 self |

### BibTeX

@ARTICLE{Mitchell99topologicalk-theory,

author = {Stephen A. Mitchell},

title = {Topological K-theory of Algebraic K-theory Spectra},

journal = {J. Algebraic K-Theory},

year = {1999},

volume = {3},

pages = {607--626}

}

### Years of Citing Articles

### OpenURL

### Abstract

Introduction One of the central problems of algebraic K-theory is to compute the K-groups K n X of a scheme X. Since these groups are, by denition, the homotopy groups of a spectrum KX, it makes sense to analyze the homotopy-type of the spectrum, rather than just the disembodied homotopy groups. In addition to facilitating the computation of the K-groups themselves, knowledge of the spectrum KX can be applied to the study of other topological invariants. For example, if X = Spec R, then the homology groups of the zero-th space 1 KX are of interest since they are the homology groups of the innite general linear group GLR; but they are not determined by the homotopy groups of KX alone. Topological complex K-theory is another important invariant. Let K denote the periodic complex K-theory spectrum, and let ^ K denote its Bouseld `-adic completion