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

v3: 30 pages; adjusted title and corrected proof of Proposition 4.15. Accepted for publication in Geometry and Topology

References in corpus (3)

• Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories
• Group completion and units in I-spaces
• Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces

Cited by in corpus (9)

• Localization sequences for logarithmic topological Hochschild homology
• Logarithmic topological Hochschild homology of topological K-theory spectra
• Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces
• Towards an understanding of ramified extensions of structured ring spectra
• Algebraic K-theory of strict ring spectra
• On the Brun spectral sequence for topological Hochschild homology
• Virtual vector bundles and graded Thom spectra
• Commutative ring spectra
• On Deformation Theory in Higher Logarithmic Geometry