Localization sequences for logarithmic topological cyclic homology
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908402076090368 |
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| author | Rognes, John Sagave, Steffen Schlichtkrull, Christian |
| author_facet | Rognes, John Sagave, Steffen Schlichtkrull, Christian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_08492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization sequences for logarithmic topological cyclic homology Rognes, John Sagave, Steffen Schlichtkrull, Christian Algebraic Topology 55P43 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. |
| title | Localization sequences for logarithmic topological cyclic homology |
| topic | Algebraic Topology 55P43 |
| url | https://arxiv.org/abs/2506.08492 |