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

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.