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Algebraic Topology and Its Applications pp 163–240Cite as

On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint

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Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 27))

Abstract

The original purpose of this paper was to give a leisurely exposition of the author’s work [Mitchell 1990a, b], including the philosophy behind it and its connection with the Lichtenbaum-Quillen conjectures. The intended audience included homotopy theorists and algebraic K-theorists. However it soon became clear that this necessitates explaining algebraic K-theory to the former group and stable homotopy theory to the latter; hence the length of the present work. The paper in fact consists of three parts: (1) an exposition of the Lichtenbaum-Quillen conjectures; (2) an introduction to the “chromatic” view of stable homotopy theory, and related topics; and (3) an account of how the first two parts are related, together with an exposition of the author’s recent work cited above. We have made an effort to assume as little as possible in the way of background, and wherever it seemed reasonable to do so, we have sketched the proofs of the main results.

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Author information

Authors and Affiliations

  1. Dept. of Math, Univ. of Washington, Seattle, WA, 98195-0001, USA

    Stephen A. Mitchell

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  1. Stephen A. Mitchell
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Gunnar E. Carlsson  & Ralph L. Cohen  & 

  2. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Wu-Chung Hsiang

  3. Mathematics Research Center, University of Warwick, CV4 7AL, Coventry, UK

    John D. S. Jones

  4. Mathematical Sciences Research Institute, 1000 Centennial Drive, 94720, Berkeley, CA, USA

    John D. S. Jones

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© 1994 Springer-Verlag New York, Inc.

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Mitchell, S.A. (1994). On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint. In: Carlsson, G.E., Cohen, R.L., Hsiang, WC., Jones, J.D.S. (eds) Algebraic Topology and Its Applications. Mathematical Sciences Research Institute Publications, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9526-3_7

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  • DOI: https://doi.org/10.1007/978-1-4613-9526-3_7

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  • Print ISBN: 978-1-4613-9528-7

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