Logarithmic structures on topological

Sagave, Steffen

doi:10.2140/gt.2014.18.447

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

Steffen Sagave

Geometry & Topology 18 (2014) 447–490

DOI: 10.2140/gt.2014.18.447

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/

Volume 18, issue 1 (2014)