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- W4385849400 abstract "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 $lambda$-rings and to motivate new results in Grothendieck's schematization program, building on work of Ekedahl, Kriz, Mandell, Lurie, Quillen, Sullivan, Toen, and Yuan. In particular, there is an $infty$-category of perfect derived $lambda$-rings with trivializations of the Adams operations $psi^p$ for all $p$ such that the functor sending a space $X$ to its integral cochains on $X$, viewed as such a derived $lambda$-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." @default.
- W4385849400 created "2023-08-16" @default.
- W4385849400 creator A5056527815 @default.
- W4385849400 date "2023-08-14" @default.
- W4385849400 modified "2023-10-16" @default.
- W4385849400 title "Spherical Witt vectors and integral models for spaces" @default.
- W4385849400 doi "https://doi.org/10.48550/arxiv.2308.07288" @default.
- W4385849400 hasPublicationYear "2023" @default.
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