Skip to content
DraconiticResearch
Search Sources API
182,460 studies31 sourcesUpdated 29 min ago
PreprintarXiv licencearXiv

Local Logarithmic Cartier Transform

  • Sami Fersi
Open at sourcePDFDOICite

Abstract

This article is the first of three articles whose goal is to generalize the Cartier transform of Ogus and Vologodsky to the logarithmic setting. In this article, we generalize a local version, due to Shiho, of the Cartier transform to log smooth schemes. More precisely, let k be a perfect field of positive characteristic and equip Speck with the trivial logarithmic structure. For a log smooth morphism of logarithmic schemes X → S, where S is log flat and locally of finite type over Speck, we obtain, under the assumption that the exact relative Frobenius lifts over the Witt vectors of k to a morphism between log smooth schemes over S, a fully faithful functor from the category of quasi-coherent modules on the base change X'=X×S,FSS of X by the Frobenius FS of S, equipped with a quasi-nilpotent Higgs field, to the category of quasi-coherent modules on X equipped with a quasi-nilpotent integrable connection. For this, we prove a log flat descent theorem for morphisms, based on previous work by Kato.

Related

  1. A Topos-Theoretic Approach to the Logarithmic Cartier Transform
    Sami Fersi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Indexed Logarithmic Cartier Transform
    Sami Fersi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. A Local Fourier-Transform Proof of Offen's Spherical Transfer Theorem
    Zhengyu Mao, Chen Wan
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds
    Xiaolong Liu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  5. Riesz transform on eventually Gaussian local trees
    Fabrice Baudoin, Aobo Chen, Li Chen
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{fersi2026local,
  title = {{Local Logarithmic Cartier Transform}},
  author = {Sami Fersi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25172},
  eprint = {2609.25172},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25172},
}
RIS
TY  - UNPB
TI  - Local Logarithmic Cartier Transform
AU  - Sami Fersi
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25172
UR  - https://arxiv.org/abs/2609.25172
AB  - This article is the first of three articles whose goal is to generalize the Cartier transform of Ogus and Vologodsky to the logarithmic setting. In this article, we generalize a local version, due to Shiho, of the Cartier transform to log smooth schemes. More precisely, let k be a perfect field of positive characteristic and equip Speck with the trivial logarithmic structure. For a log smooth morphism of logarithmic schemes X → S, where S is log flat and locally of finite type over Speck, we obtain, under the assumption that the exact relative Frobenius lifts over the Witt vectors of k to a morphism between log smooth schemes over S, a fully faithful functor from the category of quasi-coherent modules on the base change X'=X×_S,F_SS of X by the Frobenius F_S of S, equipped with a quasi-nilpotent Higgs field, to the category of quasi-coherent modules on X equipped with a quasi-nilpotent integrable connection. For this, we prove a log flat descent theorem for morphisms, based on previous work by Kato.
ER  -