Skip to content
DraconiticResearch
Search Sources API
186,631 studies31 sourcesUpdated 49 min ago
PreprintarXiv licencearXiv

A rigidity theorem for π*-étale 𝔼k-algebras

  • Xiansheng Li
Open at sourcePDFDOICite

Abstract

We prove a rigidity theorem for π*-étale 𝔼k-algebras over an 𝔼k+1-ring spectrum: the category of π*-étale extensions of an 𝔼k-algebra is identified with the ordinary category of étale Dirac algebras over its graded homotopy Dirac ring. The proof develops a relative Goerss-Hopkins type obstruction theory in synthetic spectra, including an I-complete version. As an application, the completed obstruction theory constructs the In-complete 𝔼3-MU(p)-algebra realization of the Lubin-Tate theory, hence an 𝔼4-orientation MU(p)→ En.

Related

  1. Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. II
    Kai Mao
    HALPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryAnalysis & PDEsHALarXiv
  2. Operator systems in étale groupoid C*-algebras
    Georgios Baziotis, Douglas Farenick, Evgenios T. A. Kakariadis +3
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. I
    Kai Mao
    HALPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryAnalysis & PDEsHALarXiv
  4. Morita equivalence for Lp-operator algebras associated with étale groupoids
    Yeong Chyuan Chung, Alonso Delfín, Zhen Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Scalar-mean rigidity theorem and Llarull's theorem for nonspin manifolds
    Gaoming Wang, Jinmin Wang, Zhizhang Xie +1
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{li2026rigidity,
  title = {{A rigidity theorem for $π_*$-étale $\mathbb E_k$-algebras}},
  author = {Xiansheng Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.22680},
  eprint = {2607.22680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22680},
}
RIS
TY  - UNPB
TI  - A rigidity theorem for π_*-étale 𝔼_k-algebras
AU  - Xiansheng Li
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2607.22680
UR  - https://arxiv.org/abs/2607.22680
AB  - We prove a rigidity theorem for π_*-étale 𝔼_k-algebras over an 𝔼_k+1-ring spectrum: the category of π_*-étale extensions of an 𝔼_k-algebra is identified with the ordinary category of étale Dirac algebras over its graded homotopy Dirac ring. The proof develops a relative Goerss-Hopkins type obstruction theory in synthetic spectra, including an I-complete version. As an application, the completed obstruction theory constructs the I_n-complete 𝔼_3-MU_(p)-algebra realization of the Lubin-Tate theory, hence an 𝔼_4-orientation MU_(p)→ E_n.
ER  -