Volume 18, issue 1 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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–theory spectra which approximate the respective periodic spectra. The inclusion of the p–complete Adams summand into the p–complete connective complex K–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
References
Publication
Received: 2 May 2012
Revised: 11 July 2013
Accepted: 9 August 2013
Published: 29 January 2014
Proposed: Paul Goerss
Seconded: Mark J Behrens, Ralph Cohen
Authors
Steffen Sagave
Mathematical Institute
University of Bonn
Endenicher Allee 60
53115 Bonn
Germany
http://www.math.uni-bonn.de/people/sagave/