Logarithmic structures on topological K-theory spectra

摘要

We study a modified version of Rognes' logarithmic structures on structuredring spectra. In our setup, we obtain canonical logarithmic structures onconnective K-theory spectra which approximate the respective periodic spectra.The inclusion of the p-complete Adams summand into the p-complete connectivecomplex K-theory spectrum is compatible with these logarithmic structures. Thevanishing of appropriate logarithmic topological Andre-Quillen homology groupsconfirms that the inclusion of the Adams summand should be viewed as a tamelyramified extension of ring spectra.