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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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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