paularne

• Dundas, Bjørn Ian & Østvær, Paul Arne (2026). The integral motivic dual Steenrod algebra. Mathematische Zeitschrift. ISSN 0025-5874. 313(2). doi: 10.1007/s00209-026-04044-1. Fulltekst i vitenarkiv
• Federico, Binda,; Doosung, Park, & Østvær, Paul Arne (2025). On the logarithmic slice filtration. Geometry and Topology. ISSN 1465-3060. 29, s. 2653–2693. doi: 10.2140/gt.2025.29.2653. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Bachmann, Tom; Elmanto, Elden & Østvær, Paul Arne (2025). Étale motivic spectra and Voevodsky’s convergence conjecture. Journal of the European Mathematical Society (Print). ISSN 1435-9855. 27(7), s. 2653–2704. doi: 10.4171/JEMS/1421. Fulltekst i vitenarkiv Vis sammendrag

  We prove a new convergence result for the slice spectral sequence, following work by Levine and Voevodsky. This verifies a derived variant of Voevodsky’s conjecture on convergence of the slice spectral sequence. This is, in turn, a necessary ingredient for our main theorem: a Thomason-style étale descent result for the Bott-inverted motivic sphere spectrum, which generalizes and extends previous étale descent results for special examples of motivic cohomology theories. Combined with first author’s étale rigidity results, we obtain a complete structural description of the étale motivic stable category.

• Dugger, Daniel; Dundas, Bjørn Ian; Isaksen, Daniel C. & Østvær, Paul Arne (2024). The multiplicative structures on motivic homotopy groups. Algebraic and Geometric Topology. ISSN 1472-2747. 24(3), s. 1781–1786. doi: 10.2140/agt.2024.24.1781. Fulltekst i vitenarkiv Vis sammendrag

  We reconcile the multiplications on the homotopy rings of motivic ring spectra used by Voevodsky and Dugger. While the connection is elementary and similar phenomena have been observed in situations like supersymmetry, neither we nor other researchers we consulted were aware of the conflicting definitions and the potential consequences. Hence this short note.

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• Bachmann, Tom; Calmès, Babtiste; Déglise, Frédéric; Fasel, Jean & Østvær, Paul Arne (2025). Milnor-Witt motives. American Mathematical Society (AMS). ISBN 9781470471460. doi: https:/www.ams.org/books/memo/1572/. Fulltekst i vitenarkiv

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• Østvær, Paul Arne (2025). Motivic K-theory. Fulltekst i vitenarkiv
• Østvær, Paul Arne (2025). Moivic K-theory. Fulltekst i vitenarkiv
• Østvær, Paul Arne (2024). Hermitian K-groups and motives. Fulltekst i vitenarkiv
• Østvær, Paul Arne (2024). Hermitian K-groups and motives. Fulltekst i vitenarkiv
• Østvær, Paul Arne (2024). Hermitian K-groups and motives. Fulltekst i vitenarkiv

Se alle arbeider i NVA