PreprintCC BY-NC-SA 4.0arXiv
A Note on Topological Hochschild Homology Relative to SphereW(k)[x0,x1,…,xn]
Abstract
We explain the relation between the relative topological Hochschild homology THH(R/SphereW(k)[x0,…,xn]) and the Nygaard-completed Frobenius-twisted relative prismatic cohomology Prism̂(1)R/W(k)[x0,…,xn]∧, where W(k)[x0,x1,…,xn]→ R is relatively quasiregular semiperfectoid. As an application, for R=Zp[x]/(px), we compute π*THH(R)∧p by descent along THH(R)∧p→ THH(R/Spherep[z,x]), where R is regarded as an Einfty-Spherep[z,x]-algebra via Spherep[z,x]xrightarrowz↦ p,x↦ xZp[x]/(px).
Related
- Iterated Topological Hochschild Homology of 𝔽p at odd primes
- Some chromatic height computations for homotopy fixed points of iterated topological Hochschild homology
- The Hochschild (co)homology of gentle algebras
- Hochschild homology and the derived de Rham complex revisited
- ℂ-Motivic Eilenberg-Mac Lane Spectra as MGL-Motivic Thom Spectra and Normed 𝔾m-Hochschild Homology
BibTeX
@misc{guo2026note,
title = {{A Note on Topological Hochschild Homology Relative to $\Sphere_W(k)[x_0,x_1,\ldots,x_n]$}},
author = {Jingbang Guo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.19829},
eprint = {2608.19829},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19829},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A Note on Topological Hochschild Homology Relative to Sphere_W(k)[x_0,x_1,…,x_n]
AU - Jingbang Guo
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2608.19829
UR - https://arxiv.org/abs/2608.19829
AB - We explain the relation between the relative topological Hochschild homology THH(R/Sphere_W(k)[x_0,…,x_n]) and the Nygaard-completed Frobenius-twisted relative prismatic cohomology Prism̂^(1)_R/W(k)[x_0,…,x_n]^∧, where W(k)[x_0,x_1,…,x_n]→ R is relatively quasiregular semiperfectoid. As an application, for R=Z_p[x]/(px), we compute π_*THH(R)^∧_p by descent along THH(R)^∧_p→ THH(R/Sphere_p[z,x]), where R is regarded as an Einfty-Sphere_p[z,x]-algebra via Sphere_p[z,x]xrightarrowz↦ p,x↦ xZ_p[x]/(px).
ER -