# On Bott-periodic algebraic K-theory.

Publicacions Matemàtiques (1994)

- Volume: 38, Issue: 1, page 213-225
- ISSN: 0214-1493

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topZaldívar, 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 -

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