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K(1)-Local Homotopy, Iwasawa Theory and Algebraic K-Theory

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Handbook of K-Theory

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Abstract

The Iwasawa algebra Λ is a power series ring Z ℓ[[T]], ℓ a fixed prime. It arises in number theory as the pro-group ring of a certain Galois group, and in homotopy theory as a ring of operations in ℓ-adic complex K-theory. Furthermore, these two incarnations of Λ are connected in an interesting way by algebraic K-theory. The main goal of this paper is to explore this connection, concentrating on the ideas and omitting most proofs.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA, 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, Northwestern University, 60208, Evanston, IL, USA

    Eric M. Friedlander

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    Daniel R. Grayson

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Mitchell, S. (2005). K(1)-Local Homotopy, Iwasawa Theory and Algebraic K-Theory. In: Friedlander, E., Grayson, D. (eds) Handbook of K-Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27855-9_19

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