JournalsjemsVol. 20, No. 2pp. 489–527

Logarithmic topological Hochschild homology of topological KK-theory spectra

  • John Rognes

    University of Oslo, Norway
  • Steffen Sagave

    Radboud Universiteit Nijmegen, The Netherlands
  • Christian Schlichtkrull

    University of Bergen, Norway
Logarithmic topological Hochschild homology of topological $K$-theory spectra cover

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Abstract

In this paper we continue our study of logarithmic topological Hochschild homology. We show that the inclusion of the connective Adams summand\ell into the pp-local complex connective KK-theory spectrum ku(p)ku_{(p)}, equipped with suitable log structures, is a formally log THH-étale map, and compute the V(1)V(1)-homotopy of their logarithmic topological Hochschild homology spectra. As an application, we recover Ausoni's computation of the V(1)V(1)-homotopy of the ordinary THH of kuku.

Cite this article

John Rognes, Steffen Sagave, Christian Schlichtkrull, Logarithmic topological Hochschild homology of topological KK-theory spectra. J. Eur. Math. Soc. 20 (2018), no. 2, pp. 489–527

DOI 10.4171/JEMS/772