Logarithmic topological Hochschild homology of topological K-theory spectra

Abstract

In this paper we continue our study of logarithmic topological Hochschild homology. We show that the inclusion of the connective Adams summand ℓ into the p-local complex connective K-theory spectrum ku(p), equipped with suitable log structures, is a formally log THH-´etale map, and compute the V (1)-homotopy of their logarithmic topological Hochschild ho-mology spectra. As an application, we recover Ausoni’s computation of the V (1)-homotopy of the ordinary THH of ku. This research was originally published in: Journal of the European Mathematical Society. © European Mathematical Society.