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PreprintarXiv licencearXiv

Hℤ/4 is not an 𝔼2-Thom Spectrum over the $2$-Complete Sphere Spectrum

  • Mattie Ji
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Abstract

For any prime number p, the classic Hopkins-Mahowald theorem asserts that Hℤ/p is an 𝔼2-Thom spectrum over the p-complete sphere spectrum. Kitchloo extended this result to show that Hℤ/pk is an 𝔼2-Thom spectrum over the p-local sphere spectrum, except for the case when (p, k) = (2, 2). We solve the remaining case by showing that Hℤ/4 is not an 𝔼2-Thom spectrum over the $2$-complete sphere spectrum, and consequently the $2$-local sphere spectrum. This work was developed with substantial assistance from GPT-5.6 Sol and GPT-6 Astra, and an early draft was subsequently reviewed using Claude Fable 5.1.

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Cite

BibTeXRIS
BibTeX
@misc{ji2026hℤ4,
  title = {{$H\mathbbZ/4$ is not an $\mathbbE_2$-Thom Spectrum over the $2$-Complete Sphere Spectrum}},
  author = {Mattie Ji},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19446},
  eprint = {2609.19446},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19446},
}
RIS
TY  - UNPB
TI  - Hℤ/4 is not an 𝔼_2-Thom Spectrum over the $2$-Complete Sphere Spectrum
AU  - Mattie Ji
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19446
UR  - https://arxiv.org/abs/2609.19446
AB  - For any prime number p, the classic Hopkins-Mahowald theorem asserts that Hℤ/p is an 𝔼_2-Thom spectrum over the p-complete sphere spectrum. Kitchloo extended this result to show that Hℤ/p^k is an 𝔼_2-Thom spectrum over the p-local sphere spectrum, except for the case when (p, k) = (2, 2). We solve the remaining case by showing that Hℤ/4 is not an 𝔼_2-Thom spectrum over the $2$-complete sphere spectrum, and consequently the $2$-local sphere spectrum. This work was developed with substantial assistance from GPT-5.6 Sol and GPT-6 Astra, and an early draft was subsequently reviewed using Claude Fable 5.1.
ER  -