Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 20 min ago
PreprintarXiv licencearXiv

Logarithmic Ainf-cohomology, Part II

  • Hansheng Diao
  • Zhefan Duan
  • Zijian Yao
Open at sourcePDFDOICite

Abstract

We develop a theory of logarithmic Ainf-cohomology with coefficients for a class of p-adic log formal schemes that are ``sufficiently log smooth'', where the coefficients are given by relative log BKF modules. Then we establish comparison isomorphisms with étale, de Rham, and crystalline cohomology, and also extend these results to the derived setting. As an application, we give a new proof of the Cst conjecture for semistable local systems. The proof also uses the prismatic interpretation of semistable local systems established by Du--Liu--Moon--Shimizu.

Related

  1. On Logarithmic Poisson and De Rham Cohomology Groups of a Class of Inhomogeneous Divisors
    Kamtila Kari, Dongho Joseph, Diekouam Fotso Luc Emery
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Computations of Cohomology of Arithmetic Groups, Part 1
    Ivan Horozov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Boundary layer analysis for the 2D Chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part II. viscous vanishing limit
    Hui Wang, Lingling Zhao
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. On the Leibniz cohomology of vector fields
    Alessandra Frabetti, Friedrich Wagemann
    Annals of Global Analysis and GeometryPeer-reviewedPublisher termsFull text1 citedMathematical physicsHAL
  5. Igusa stacks and the cohomology of Shimura varieties
    Patrick Daniels, Pol van Hoften, Dongryul Kim +1
    Inventiones mathematicaePeer-reviewedLicence not statedFull text30 citedAlgebra & number theoryMathematical physicsOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{diao2026logarithmic,
  title = {{Logarithmic $A_\mathrminf$-cohomology, Part II}},
  author = {Hansheng Diao and Zhefan Duan and Zijian Yao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07737},
  eprint = {2609.07737},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07737},
}
RIS
TY  - UNPB
TI  - Logarithmic A_inf-cohomology, Part II
AU  - Hansheng Diao
AU  - Zhefan Duan
AU  - Zijian Yao
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07737
UR  - https://arxiv.org/abs/2609.07737
AB  - We develop a theory of logarithmic A_inf-cohomology with coefficients for a class of p-adic log formal schemes that are ``sufficiently log smooth'', where the coefficients are given by relative log BKF modules. Then we establish comparison isomorphisms with étale, de Rham, and crystalline cohomology, and also extend these results to the derived setting. As an application, we give a new proof of the C_st conjecture for semistable local systems. The proof also uses the prismatic interpretation of semistable local systems established by Du--Liu--Moon--Shimizu.
ER  -