On the logarithmic slice filtration
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916906566418432 |
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| author | Binda, Federico Park, Doosung Østvær, Paul Arne |
| author_facet | Binda, Federico Park, Doosung Østvær, Paul Arne |
| contents | We consider slice filtrations in logarithmic motivic homotopy theory. Our main results establish conjectured compatibilities with the Beilinson, BMS, and HKR filtrations on (topological, log) Hochschild homology and related invariants. In the case of perfect fields admitting resolution of singularities, we show that the slice filtration realizes the BMS filtration on the $p$-completed topological cyclic homology. Furthermore, the motivic trace map is compatible with the slice and BMS filtrations, yielding a natural morphism from the motivic slice spectral sequence to the BMS spectral sequence. Finally, we consider the Kummer étale hypersheafification of logarithmic $K$-theory and show that its very effective slices compute Lichtenbaum étale motivic cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the logarithmic slice filtration Binda, Federico Park, Doosung Østvær, Paul Arne Algebraic Geometry K-Theory and Homology We consider slice filtrations in logarithmic motivic homotopy theory. Our main results establish conjectured compatibilities with the Beilinson, BMS, and HKR filtrations on (topological, log) Hochschild homology and related invariants. In the case of perfect fields admitting resolution of singularities, we show that the slice filtration realizes the BMS filtration on the $p$-completed topological cyclic homology. Furthermore, the motivic trace map is compatible with the slice and BMS filtrations, yielding a natural morphism from the motivic slice spectral sequence to the BMS spectral sequence. Finally, we consider the Kummer étale hypersheafification of logarithmic $K$-theory and show that its very effective slices compute Lichtenbaum étale motivic cohomology. |
| title | On the logarithmic slice filtration |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2403.03056 |