Logarithmic topological Hochschild homology of topological K-theory spectra

TL;DR

This paper advances the understanding of logarithmic topological Hochschild homology (log THH) by analyzing the log structures of K-theory spectra, computing their V(1)-homotopy, and connecting to known results in algebraic K-theory.

Contribution

It demonstrates that the inclusion of the connective Adams summand into p-local complex K-theory is a formally log THH-etale map and computes the V(1)-homotopy of their log THH spectra, extending prior work.

Findings

The inclusion map is a formally log THH-etale map.

Computed the V(1)-homotopy of the log THH spectra.

Reproduced Ausoni's computation of the V(1)-homotopy of THH of ku.

Abstract

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