PreprintarXiv licencearXiv
Some chromatic height computations for homotopy fixed points of iterated topological Hochschild homology
Abstract
For an 𝔼∞-ring spectrum R of chromatic height k, the trace method and the chromatic redshift imply that Tn-fixed point of n-fold iterated topological Hochschild homology of R has chromatic height at most k+n. In this paper, we compute these heights for H𝔽p, Hℤ and the p-complete connective image-of-J spectrum jp for all primes and n≥1, which are exactly n−1, n and n+1, respectively. Our method is based on properties of Wilson spaces and relative topological Hochschild homology over MU.
Related
- Iterated Topological Hochschild Homology of 𝔽p at odd primes
- A Note on Topological Hochschild Homology Relative to SphereW(k)[x0,x1,…,xn]
- On smooth and bundle structures on topological manifolds homotopy equivalent to S4k−1-bundles over S4k
- The Hochschild (co)homology of gentle algebras
- Hochschild cohomology of Hilbert schemes of points on surfaces
BibTeX
@misc{zha2026some,
title = {{Some chromatic height computations for homotopy fixed points of iterated topological Hochschild homology}},
author = {Jiaxi Zha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33534},
eprint = {2610.33534},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33534},
}
RIS
TY - UNPB
TI - Some chromatic height computations for homotopy fixed points of iterated topological Hochschild homology
AU - Jiaxi Zha
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33534
UR - https://arxiv.org/abs/2610.33534
AB - For an 𝔼_∞-ring spectrum R of chromatic height k, the trace method and the chromatic redshift imply that T^n-fixed point of n-fold iterated topological Hochschild homology of R has chromatic height at most k+n. In this paper, we compute these heights for H𝔽_p, Hℤ and the p-complete connective image-of-J spectrum j_p for all primes and n≥1, which are exactly n−1, n and n+1, respectively. Our method is based on properties of Wilson spaces and relative topological Hochschild homology over MU.
ER -