#### Date of Award

1986

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### Abstract

Let K(,*)(A; /L('n)) denote the mod-L('n) algebraic K-theory of a 1/L -algebra A. V. Snaith has studied Bott-periodic algebraic K-theory K(,i)(A; /L('n)) 1/(beta)(,n) , the direct limit of iterated multiplications by (beta)(,n), the 'Bott element', using the K-theory product. For L an odd prime, Snaith has given a description of K(,*)(A; /L('n))(1/(beta)(,n)) using Adams maps between Moore spectra. These constructions are interesting, in particular, for their connections with the Lichtenbaum-Quillen conjecture.;In this thesis we obtain an analogous description of K(,*)(A; /2('n)) 1/(beta)(,n) , n (GREATERTHEQ) 2, for an algebra A with 1/2 (ELEM) A and such that A contains a fourth root of unity. We approach this problem using low dimen- sional computations of the stable homotopy groups of B /4, and transfer arguments to show that a power of the mod-4 'Bott element' is induced by an Adams map.

#### Recommended Citation

Zaldivar-cruz, Felipe De, "Localized Algebraic K-theory" (1986). *Digitized Theses*. 1521.

https://ir.lib.uwo.ca/digitizedtheses/1521