Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 24 min ago
PreprintarXiv licencearXiv

Noetherian local rings without perfectoid towers

  • Tatsuki Yamaguchi
Open at sourcePDFDOICite

Abstract

Let k be a perfect field of characteristic p>0. We prove that if a p-torsionfree ring R, defined by homogeneous equations over W(k), admits a perfectoid tower arising from (R,(p)), then its special fiber is F-liftable. We also give explicit examples admitting no such tower, including examples with F-liftable special fibers.

Related

  1. Decomposition Theorem for Perfectoid Rings along General Ideals
    Ryo Ishizuka, Léo Navarro Chafloque
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. On the iso-Artinianness of one-dimensional Noetherian rings
    Xiaolei Zhang, Ran Yan, Wei Qi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. On Z-Noetherian Rings
    Ambar Dubey, Tushar Singh, Shiv Datt Kumar
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Which posets are spectra of Noetherian rings? The case of height at most one
    Xin Li
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. A Fitting criterion for quasi-Gorenstein local rings
    Sora Miyashita
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{yamaguchi2026noetherian,
  title = {{Noetherian local rings without perfectoid towers}},
  author = {Tatsuki Yamaguchi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32577},
  eprint = {2610.32577},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32577},
}
RIS
TY  - UNPB
TI  - Noetherian local rings without perfectoid towers
AU  - Tatsuki Yamaguchi
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32577
UR  - https://arxiv.org/abs/2610.32577
AB  - Let k be a perfect field of characteristic p>0. We prove that if a p-torsionfree ring R, defined by homogeneous equations over W(k), admits a perfectoid tower arising from (R,(p)), then its special fiber is F-liftable. We also give explicit examples admitting no such tower, including examples with F-liftable special fibers.
ER  -