On Bott-periodic algebraic K-theory.

Zaldívar, Felipe. "On Bott-periodic algebraic K-theory.." Publicacions Matemàtiques 38.1 (1994): 213-225. <http://eudml.org/doc/41192>.

@article{Zaldívar1994,
abstract = {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.},
author = {Zaldívar, Felipe},
journal = {Publicacions Matemàtiques},
keywords = {Homotopía; Topología algebraica; Homología generalizada; mod- algebraic -theory of a -algebra; Bott-periodic algebraic -theory; stable homotopy groups of ; Bott element; Adams maps between Moore spectra; transfer},
language = {eng},
number = {1},
pages = {213-225},
title = {On Bott-periodic algebraic K-theory.},
url = {http://eudml.org/doc/41192},
volume = {38},
year = {1994},
}

TY - JOUR
AU - Zaldívar, Felipe
TI - On Bott-periodic algebraic K-theory.
JO - Publicacions Matemàtiques
PY - 1994
VL - 38
IS - 1
SP - 213
EP - 225
AB - 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.
LA - eng
KW - Homotopía; Topología algebraica; Homología generalizada; mod- algebraic -theory of a -algebra; Bott-periodic algebraic -theory; stable homotopy groups of ; Bott element; Adams maps between Moore spectra; transfer
UR - http://eudml.org/doc/41192
ER -