Galois reconstruction of Artin–Tate ℝ-motivic spectra

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