Galois reconstruction of Artin–Tate ℝ-motivic spectra
- 1Department of Mathematical Sciences, University of Copenhagen, Denmark
- 2Mathematics Department, Massachusetts Institute of Technology, Cambridge, MA, United States
- 3Department of Mathematics, Harvard University, Cambridge, MA, United States, Department of Mathematics, University of Maryland, College Park, MD, United States
Abstract
We explain how to reconstruct the category of Artin-Tate R-motivic spectra as a deformation of the purely topological C 2 -equivariant stable category.The special fiber of this deformation is algebraic, and equivalent to an appropriate category of C 2 -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 R-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.1. Introduction 1625 2. Constructing the element ta 1644 3. The ta-local category 1646 4. Galois reconstruction 1652 5. Modules over the cofiber of ta 1660 6.The Chow t-structure and R 1676 7. The a-local category 1687 8. Completions 1691 9. Odd primes 1696 10.Examples and computations 1699 Appendix A. Recollections on compact rigid generation 1703 Appendix B. Recollections on filtered objects 1706 Appendix C. A machine for deforming homotopy theories 1708
Related
- Tate and Artin--Tate Motivic Tensor-Triangular Geometry
- Spectral Beurling-Selberg Approximation and Applications to Effective Motivic Chebotarev-Sato-Tate Estimates
- Lubin-Tate representations over nontrivial finite Galois extensions of ℚp are not Aut-intrinsically Hodge-Tate
- On the observability of Galois representations and the Tate conjecture
- Anabelian presentation of the motivic Galois group in characteristic zero
BibTeX
@article{burklund2026galois,
title = {{Galois reconstruction of Artin–Tate ℝ-motivic spectra}},
author = {Robert Burklund and Jeremy Hahn and Andrew Senger},
journal = {Geometry \& Topology},
year = {2026},
month = jul,
doi = {10.2140/gt.2026.30.1625},
url = {https://doi.org/10.2140/gt.2026.30.1625},
note = {CC BY},
}
RIS
TY - JOUR
TI - Galois reconstruction of Artin–Tate ℝ-motivic spectra
AU - Robert Burklund
AU - Jeremy Hahn
AU - Andrew Senger
PY - 2026
DA - 2026/07/18
JO - Geometry & Topology
DO - 10.2140/gt.2026.30.1625
UR - https://doi.org/10.2140/gt.2026.30.1625
AB - We explain how to reconstruct the category of Artin-Tate R-motivic spectra as a deformation of the purely topological C 2 -equivariant stable category.The special fiber of this deformation is algebraic, and equivalent to an appropriate category of C 2 -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 R-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.1. Introduction 1625 2. Constructing the element ta 1644 3. The ta-local category 1646 4. Galois reconstruction 1652 5. Modules over the cofiber of ta 1660 6.The Chow t-structure and R 1676 7. The a-local category 1687 8. Completions 1691 9. Odd primes 1696 10.Examples and computations 1699 Appendix A. Recollections on compact rigid generation 1703 Appendix B. Recollections on filtered objects 1706 Appendix C. A machine for deforming homotopy theories 1708
SN - 1364-0380
SN - 1465-3060
ER -