On 2-primary localized algebraic \(K\)-theory (Q2721262)

Let \(A\) be a commutative algebra over \({\mathbb{Z}}[1/2, \sqrt{-1}]\) and let \(K_{*}(A ; {\mathbb{Z}}/2^{n})\) denote the algebraic \(K\)-theory of \(A\) with mod \(2^{n}\) coefficients. Let \(\beta_{2n}\) denote the \(\operatorname {mod}2^{n}\) ``Bott element'' [\textit{W. G. Dwyer, E. M. Friedlander, V. P. Snaith} and \textit{R. W. Thomason}, Invent. Math. 66, 481-491 (1982; Zbl 0501.14013) and \textit{V. P. Snaith}, Lect. Notes Math. 1051, 128-155 (1984; Zbl 0551.18004)]. \textit{F. Zaldívar} [Publ. Mat., Barc. 38, No. 1, 213-225 (1994; Zbl 0829.55003)] showed, when \(n \geq 2\), that the localisation \(K_{*}(A ; {\mathbb{Z}}/2^{2n})[1/\beta_{2n}]\) is isomorphic to the localisation obtained by inverting Adams map \(A_{1} : \Sigma^{*}P(2^{2n}) \rightarrow P(2^{2n})\) of Moore spectra. In this note he extends the result to the case when \(n=1\).NEWLINENEWLINEFor the entire collection see [Zbl 0948.00027].