The Algebraic K-Theory Spectrum of a 2-Adic Local Field

Mitchell, Stephen A.

Department of Mathematics, University of Washington, Seattle, WA 98195, U.S.A.

K-Theory 25(1):p 1-37, January 2002.

We explicitly determine the homotopy type of the 2-completed algebraic K-theory spectrum KF, where F is an arbitrary finite extension of the 2-adic rational numbers. The answer is formulated in terms of topological complex K-theory and the K-theory of suitable finite fields, suspended copies of which are glued together by connecting maps that depend on the Iwasawa theory of F.