Year: 2025
Type: article
Abstract: 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.14A21, 14F30, 14F42; 19E20 1. Introduction 2653 2. Slices for logarithmic motives 2660 3. Slice filtration on K-theory 2664 4. HKR filtration on logarithmic Hochschild homology 2666 5. BMS filtration on logarithmic topological Hochschild homology 2672 6.The characteristic-p case 2680 7. Very effective slices of Kummer étale K-theory 2685
Source: Geometry & Topology
Authors: Federico Binda, Doosung Park, Paul Arne Østvær
Institutions: University of Milan, University of Wuppertal, University of Oslo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: European Commission
Award: G972786147
OpenAlex ID: W4413315309