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Galois reconstruction of
Artin–Tate $\mathbb{R}$-motivic spectra
Robert Burklund, Jeremy Hahn and Andrew Senger |
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Geometry & Topology 30 (2026) 1625–1717
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Abstract |
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We explain how to reconstruct the category of Artin–Tate -motivic spectra as a deformation of the purely topological -equivariant stable category. The special fiber of this deformation is algebraic, and equivalent to an appropriate category of -equivariant sheaves on the moduli stack of formal groups. As such, our results directly generalize the cofiber of philosophy of Gheorghe, Isaksen, Wang and Xu. A key observation is that the Artin–Tate subcategory of -motivic spectra is easier to understand than the previously studied cellular subcategory. In particular, the Artin–Tate category contains a variant of the map, which is a feature conspicuously absent from the cellular category. |
Keywords
synthetic spectra, motivic homotopy theory, equivariant
homotopy theory
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Mathematical Subject Classification
Primary: 14F42
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References |
Publication
Received: 1 February 2023
Revised: 29 July 2025
Accepted: 29 August 2025
Published: 18 July 2026
Proposed: Stefan Schwede
Seconded: Marc Levine, Haynes R Miller
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Authors |
| Robert Burklund | |
| Department of Mathematical
Sciences University of Copenhagen Denmark |
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| Jeremy Hahn | |
| Mathematics Department Massachusetts Institute of Technology Cambridge, MA United States |
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| Andrew Senger | |
| Department of Mathematics Harvard University Cambridge, MA United States |
Department of Mathematics University of Maryland College Park, MD United States |
| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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