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Galois reconstruction of Artin-Tate mathbb{R}-motivic spectra

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arxiv 2010.10325 v2 pith:BFGL3GOA submitted 2020-10-20 math.AT math.AGmath.KT

Galois reconstruction of Artin-Tate mathbb{R}-motivic spectra

Robert Burklund , Jeremy Hahn , Andrew Senger This is my paper
classification math.AT math.AGmath.KT
keywords categoryartin-tatemathbbmotivicspectracellulardeformationequivariant
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We explain how to reconstruct the category of Artin-Tate $\mathbb{R}$-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 $\tau$ philosophy that has revolutionized classical stable homotopy theory. A key observation is that the Artin-Tate subcategory of $\mathbb{R}$-motivic spectra is easier to understand than the previously studied cellular subcategory. In particular, the Artin-Tate category contains a variant of the $\tau$ map, which is a feature conspicuously absent from the cellular category.

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