2023/08/14 by Benjamin Antieau, Antieau, Benjamin · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2308.07288
openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new construction of the spherical Witt vector functor of Lurie and Burklund-Schlank-Yuan and extend it to nonconnective objects using synthetic spectra and recent work of Holeman. The spherical Witt vectors are used to build spherical versions of perfect λ-rings and to motivate new results in Grothendieck's schematization program, building on work of Ekedahl, Kriz, Mandell, Lurie, Quillen, Sullivan, Toën, and Yuan. In particular, there is an ∞-category of perfect derived λ-rings with trivializations of the Adams operations ψp for all p such that the functor sending a space X to its integral cochains on X, viewed as such a derived λ-ring, is fully faithful on a large class of nilpotent spaces. Our theorem is closely related to recent work of Horel and Kubrak-Shuklin-Zakharov. Finally, we answer two questions of Yuan on spherical cochains.