#### Volume 18, issue 1 (2014)

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Logarithmic structures on topological $K\!$–theory spectra

### Steffen Sagave

Geometry & Topology 18 (2014) 447–490
##### Abstract

We study a modified version of Rognes’ logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective $K\phantom{\rule{0.3em}{0ex}}$–theory spectra which approximate the respective periodic spectra. The inclusion of the $p$–complete Adams summand into the $p$–complete connective complex $K\phantom{\rule{0.3em}{0ex}}$–theory spectrum is compatible with these logarithmic structures. The vanishing of appropriate logarithmic topological André–Quillen homology groups confirms that the inclusion of the Adams summand should be viewed as a tamely ramified extension of ring spectra.

##### Keywords
symmetric spectra, log structures, $E$–infinity spaces, group completion, topological André–Quillen homology
##### Mathematical Subject Classification 2010
Primary: 55P43
Secondary: 14F10, 55P47
##### Publication
Received: 2 May 2012
Revised: 11 July 2013
Accepted: 9 August 2013
Published: 29 January 2014