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On
the logarithmic slice filtration
Federico Binda, Doosung Park and Paul Arne Østvær |
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Geometry & Topology 29 (2025) 2653–2693
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Abstract |
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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 -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 -theory and show that its very effective slices compute Lichtenbaum étale motivic cohomology. |
Keywords
slice filtration, topological Hochschild homology, motivic
homotopy theory, logarithmic geometry
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Mathematical Subject Classification
Primary: 14A21, 14F30, 14F42
Secondary: 19E20
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References |
Publication
Received: 7 April 2024
Revised: 30 October 2024
Accepted: 21 December 2024
Published: 14 August 2025
Proposed: Arend Bayer
Seconded: Stefan Schwede, Marc Levine
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Authors |
| Federico Binda | |
| Dipartimento di Matematica “Federigo
Enriques” Università degli Studi di Milano Milan Italy |
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| Doosung Park | |
| Department of Mathematics and
Informatics University of Wuppertal Wuppertal Germany |
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| Paul Arne Østvær | |
| Dipartimento di Matematica “Federigo
Enriques” Università degli Studi di Milano Milan Italy |
Department of Mathematics University of Oslo Oslo Norway |
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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