\(\ell\)-adic and \({\mathbb{Z}}/\ell ^{\infty}\)-algebraic and topological K-theory. (English) Zbl 0547.18003

The author shows that if A is a commutative \({\mathbb{Z}}[1/\ell,\xi_{\ell^{\infty}}]\)-algebra, that commutative diagrams exist which generalize the one constructed in [Algebraic Topology, Proc. Conf., Aarhus 1982, Lect. Notes Math. 1051, 128-155 (1984; Zbl 0551.18004)]. Furthermore, these diagrams fit together coherently as one takes \(\lim_{\leftarrow_{\nu}}\) or \(\lim_{\to_{\nu}}\) of them. The author explains how ker \(\rho_{\nu}\) is expected to be zero (for reasonable A) and that these diagrams serve to characterize \(\ker(\lim_{\leftarrow_{\nu}} \rho_{\nu})\) and \(\ker(\lim_{\to_{\nu}} \rho_{\nu})\) in terms of the KU-theory Hurewicz homomorphism.


18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
55N15 Topological \(K\)-theory


Zbl 0551.18004
Full Text: DOI


[1] DOI: 10.1007/BF01389225 · Zbl 0501.14013
[2] Grayson, Higher Algebraic K-theory pp 217– · Zbl 0362.18015
[3] Adams, Stable Homotopy and Generalised Homology (1974)
[4] DOI: 10.1016/0040-9383(66)90004-8 · Zbl 0145.19902
[5] Weibel, Mayer–Vietoris Sequences pp 390–
[6] Thomason, Proc. Current Trends in Algebraic Topology pp 117– (1982)
[7] Thomason, Algebraic (1981)
[8] Snaith, Algebraic Top. Conf., Aarhus pp 128– (1982)
[9] Snaith, Dyer–Lashof Operations in K-theory pp 100–
[10] May, E
[11] May, Geometry of Iterated Loopspaces
[12] DOI: 10.1017/S0305004100059934 · Zbl 0508.55021
[13] DOI: 10.1007/BF01173051 · Zbl 0322.55030
[14] DOI: 10.1090/S0273-0979-1983-15086-3 · Zbl 0517.55013
[15] Loday, Ann. Sci. EC. Norm. Sup 4 9 pp 309– (1976)
[16] Hodgkin, Illinois J. Math (2) 22 pp 270– (1978)
[17] Browder, Algebraic pp 40– (1978)
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