Localization sequences for logarithmic topological cyclic homology

Abstract We introduce the notion of an ‐ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories. Our approach is based on Thom ‐algebras. It extends and strengthens our earlier work on the subject in several regards. Our examples include the fraction field of topological ‐theory, the existence of which was suggested by calculations by Ausoni and the first author. To illustrate the computational accessibility of log and log , we determine these for non‐negative even periodic sphere spectra, with their canonical prelogarithmic structures.