Logarithmic structures on topological K-theory spectra

TL;DR

This paper develops a modified framework for logarithmic structures on topological K-theory spectra, establishing canonical structures on connective spectra and analyzing their properties and extensions.

Contribution

It introduces a new approach to logarithmic structures on K-theory spectra, demonstrating compatibility with Adams summands and confirming tamely ramified extensions.

Findings

Canonical logarithmic structures on connective K-theory spectra

Compatibility of Adams summand inclusion with these structures

Vanishing of logarithmic topological Andre-Quillen homology groups

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 Andre-Quillen homology groups confirms that the inclusion of the Adams summand should be viewed as a tamely ramified extension of ring spectra.