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.
From: Steffen Sagave [view email]
[v1]
Tue, 10 Jun 2025 06:36:31 UTC (72 KB)
[v2]
Thu, 25 Jun 2026 12:15:55 UTC (73 KB)
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