On the logarithmic slice filtration

Binda, Federico¹ ; Park, Doosung² ; Østvær, Paul Arne³

¹Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Milan, Italy
²Department of Mathematics and Informatics, University of Wuppertal, Wuppertal, Germany
³Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Milan, Italy, Department of Mathematics, University of Oslo, Oslo, Norway

Geometry & topology, Tome 29 (2025) no. 5, pp. 2653-2693

Résumé

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.

Détail

DOI : 10.2140/gt.2025.29.2653

Keywords: slice filtration, topological Hochschild homology, motivic homotopy theory, logarithmic geometry

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