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arXiv · 2506.08492

Localization sequences for logarithmic topological cyclic homology

John Rognes·Steffen Sagave·Christian Schlichtkrull
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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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John Rognes, Steffen Sagave, Christian Schlichtkrull. 2025-06-10. Localization sequences for logarithmic topological cyclic homology. https://doi.org/10.1112/topo.70090

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