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Generalized Thom Spectra, Conjugate Stacks, and truncated Brown-Peterson Spectra

  • Preston Cranford
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Abstract

We propose a of definition conjugate stack for a class of suitable 𝔼3-MU-algebras that includes the truncated Brown-Peterson spectra BP⟨ n ⟩ for all heights n. Then we calculate part of BP⟨ n ⟩conj as a quotient stack in terms of Witt vectors. To perform this computation we study generalized Thom spectra and their relative Topological Hochschild Homology. We exhibit the Eilenberg-Mac Lane spectrum H𝔽2 as a 𝔼3-MU-Thom spectrum, the p-local Eilenberg-Mac Lane spectra Hℤ/pn (except for Hℤ/4) and Hℤ(p) as 𝔼3-MU(p)-Thom spectra, and the connective complex K-theory spectrum ku as 𝔼1-MU-Thom spectra. We accompany these ``go" results with ``no-go" results that show these ``go" results do not admit 𝔼∞-refinements.

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Cite

BibTeXRIS
BibTeX
@misc{cranford2026generalized,
  title = {{Generalized Thom Spectra, Conjugate Stacks, and truncated Brown-Peterson Spectra}},
  author = {Preston Cranford},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18754},
  eprint = {2610.18754},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18754},
}
RIS
TY  - UNPB
TI  - Generalized Thom Spectra, Conjugate Stacks, and truncated Brown-Peterson Spectra
AU  - Preston Cranford
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18754
UR  - https://arxiv.org/abs/2610.18754
AB  - We propose a of definition conjugate stack for a class of suitable 𝔼_3-MU-algebras that includes the truncated Brown-Peterson spectra BP⟨ n ⟩ for all heights n. Then we calculate part of BP⟨ n ⟩^conj as a quotient stack in terms of Witt vectors. To perform this computation we study generalized Thom spectra and their relative Topological Hochschild Homology. We exhibit the Eilenberg-Mac Lane spectrum H𝔽_2 as a 𝔼_3-MU-Thom spectrum, the p-local Eilenberg-Mac Lane spectra Hℤ/p^n (except for Hℤ/4) and Hℤ_(p) as 𝔼_3-MU_(p)-Thom spectra, and the connective complex K-theory spectrum ku as 𝔼_1-MU-Thom spectra. We accompany these ``go" results with ``no-go" results that show these ``go" results do not admit 𝔼_∞-refinements.
ER  -