15 April 2024 The second stable homotopy groups of motivic spheres
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
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Duke Math. J. 173(6): 1017-1084 (15 April 2024). DOI: 10.1215/00127094-2023-0023

Abstract

We compute the Milnor–Witt 2-stem of stable homotopy groups of motivic spheres over fields of characteristic not 2 in terms of motivic cohomology and hermitian K-groups. The answer reveals new relations among algebraic cycles, algebraic vector bundles equipped with quadratic forms, and stable motivic stems.

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Oliver Röndigs. Markus Spitzweck. Paul Arne Østvær. "The second stable homotopy groups of motivic spheres." Duke Math. J. 173 (6) 1017 - 1084, 15 April 2024. https://doi.org/10.1215/00127094-2023-0023

Information

Received: 4 March 2023; Revised: 4 March 2023; Published: 15 April 2024
First available in Project Euclid: 20 May 2024

Digital Object Identifier: 10.1215/00127094-2023-0023

Subjects:
Primary: 14F42

Keywords: motivic cohomology , slice filtration , Stable homotopy groups of motivic spheres

Rights: Copyright © 2024 Duke University Press

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Vol.173 • No. 6 • 15 April 2024
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