Let K*(A;Z/ln) denote the mod-ln algebraic K-theory of a Z[1/l]-algebra A. Snaith ([14], [15], [16]) has studied Bott-periodic algebraic theory Ki(A;Z/ln)[1/βn], a localized version of K*(A;Z/ln) obtained by inverting a Bott element βn . For l an odd prime, Snaith has given a description of K*(A;Z/ln)[1/βn] using Adams maps between Moore spectra. These constructions are interesting, in particular for their connections with Lichtenbaum-Quillen conjecture [16].
In this paper we obtain a description of K*(A;Z/2n)[1/βn], n ≥ 2, for an algebra A with 1/2 ∈ A and √-1 ∈ A. We approach this problem using low dimensional computations of the stable homotopy groups of BZ/4, and transfer arguments to show that a power of the mod-4 Bott element is induced by an Adams map.
@article{urn:eudml:doc:41192,
title = {On Bott-periodic algebraic K-theory.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {213-225},
mrnumber = {MR1291964},
zbl = {0829.55003},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41192}
}
Zaldívar, Felipe. On Bott-periodic algebraic K-theory.. Publicacions Matemàtiques, Tome 38 (1994) pp. 213-225. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41192/