Galois reconstruction of Artin-Tate mathbb{R}-motivic spectra
read the original abstract
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.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Higher algebra in $t$-structured tensor triangulated $\infty$-categories
Higher algebra notions are generalized to t-structured tensor triangulated ∞-categories, with analogues of Lazard's theorem, Cohn localizations, almost ring theory, étale rigidity, and a moduli characterization under ...
-
Profinite Borel completeness and smooth Artin motives
Extends Voevodsky's theorem by identifying Nisnevich smooth Artin motives with modules over the Bredon cohomology spectrum of π₁^ét(S) and shows étale variants differ exactly by sheaf vs hypersheaf distinctions on fin...
-
A Nilpotence Theorem for Rational Rigid 2-Rings of Moderate Growth
Proves a nilpotence theorem for rational rigid 2-rings of moderate growth and shows such categories have enough tt-fields of the form Perf(L) for even 2-periodic fields L.
-
Special Values without Semi-Simplicity Via K-Theory
Introduces arithmetic C(S^1,R)-modules whose K_0 yields Euler characteristics for perfect etale Z_l-sheaves and prismatic F-gauges without Tate semi-simplicity, removing the assumption from Milne's cohomological zeta-...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.