Logarithmic structures on topological

Sagave, Steffen¹

¹ Mathematical Institute, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Geometry & topology, Tome 18 (2014) no. 1, pp. 447-490.

Résumé

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.

Détail

DOI : 10.2140/gt.2014.18.447

Classification : 55P43, 14F10, 55P47
Keywords: symmetric spectra, log structures, $E$–infinity spaces, group completion, topological André–Quillen homology

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