On Bott-periodic algebraic K-theory.

Título inglés On Bott-periodic algebraic K-theory.
Título español Teoría K algebraica periódica de Bott.
Autor/es Zaldívar, Felipe
Organización Dep. Mat. Univ. Autón. Metrop. I, México D.F., Méjico
Revista 0214-1493
Publicación 1994, 38 (1): 213-225, 20 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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 Î A and √-1 Î 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.
Clasificación UNESCO 121007
Palabras clave español Homotopía ; Topología algebraica ; Homología generalizada
Código MathReviews MR1291964
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