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

In: Handbook of K-Theory

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  • Stephen A. Mitchell

    (University of Washington, Department of Mathematics)

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.

Suggested Citation

  • Stephen A. Mitchell, 2005. "K(1)-Local Homotopy, Iwasawa Theory and Algebraic K-Theory," Springer Books, in: Eric M. Friedlander & Daniel R. Grayson (ed.), Handbook of K-Theory, chapter 0, pages 955-1010, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27855-9_19
    DOI: 10.1007/978-3-540-27855-9_19
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