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On the Whitehead
theorem for nilpotent motivic spaces
Aravind Asok, Tom Bachmann and Michael J. Hopkins |
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Vol. 10 (2025), No. 4, 673–706
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Abstract |
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We improve some foundational connectivity results and the relative Hurewicz theorem in motivic homotopy theory, study functorial central series in motivic local group theory, establish the existence of functorial Moore–Postnikov factorizations for nilpotent morphisms of motivic spaces under a mild technical hypothesis and establish an analog of the Whitehead theorem for nilpotent motivic spaces. As an application, we deduce a surprising unstable motivic periodicity result. |
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Keywords
motivic, Whitehead, homotopy, nilpotent
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Mathematical Subject Classification
Primary: 14F42, 20F19, 55S45
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Milestones
Received: 2 April 2024
Revised: 25 June 2025
Accepted: 3 October 2025
Published: 28 November 2025
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Authors |
| Aravind Asok | |
| Department of Mathematics University of Southern California Los Angeles, CA United States |
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| Tom Bachmann | |
| Institut für Mathematik Johannes Gutenberg-Universität Mainz Mainz Germany |
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| Michael J. Hopkins | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
