Logarithmic THH with a chosen direction is shown to be the same as the abstract cofiber of the transfer map, resolving a conjecture of Rognes.
Localization sequences for logarithmic topological cyclic homology
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abstract
We introduce the notion of an E_k-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 R-algebras. It extends and strengthens our earlier work on the subject in several regards. Our examples include the fraction field of topological K-theory, the existence of which was suggested by calculations by Ausoni and the first author. To illustrate the computational accessibility of log THH and log TC, we determine these for non-negative even periodic sphere spectra, with their canonical prelogarithmic structures.
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On the Residue Sequence in Logarithmic Topological Cyclic Homology
Logarithmic THH with a chosen direction is shown to be the same as the abstract cofiber of the transfer map, resolving a conjecture of Rognes.