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Stable homotopy groups of motivic spheres

Oliver Röndigs and Markus Spitzweck

Vol. 6 (2025), 197–246
Abstract

These lecture notes are based on lectures given by the authors at the autumn school “Computations in motivic homotopy theory” at Regensburg University during September 16–20, 2019. Main results include a computation of the first Milnor–Witt stem of stable homotopy groups of motivic spheres over a field, presented differently than Röndigs, Spitzweck and Østvær (2019), and a partial computation of the zeroth Milnor–Witt stem of stable homotopy groups of motivic spheres over discrete valuation rings of mixed characteristic after inverting the residue characteristic.

Keywords
motivic stable homotopy, motivic cohomology, slice filtration
Mathematical Subject Classification
Primary: 14F42
Secondary: 13F30, 55P42
Milestones
Received: 11 May 2022
Revised: 18 September 2023
Accepted: 18 September 2023
Published: 15 March 2025
Authors
Oliver Röndigs
Institut für Mathematik
Universität Osnabrück
Osnabrück
Germany
Markus Spitzweck
Institut für Mathematik
Universität Osnabrück
Osnabrück
Germany