Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 38 min ago
PreprintCC BY 4.0arXiv

Generic Hodge and special Hodge--Witt polygons

  • Yuan Yang
Open at sourcePDFDOICite

Abstract

We show that, in equal characteristic p, the Hodge-Witt polygon can only move down and domino numbers can only increase under specialization in smooth proper families. We also show that the Hodge polygon of the generic fiber of a proper smooth p-adic formal scheme over 𝒪C lies on or above the Hodge-Witt polygon of its special fiber, where C is a complete algebraically closed extension of ℚp. We further show that, in this mixed-characteristic setting, if the crystalline cohomology of the special fiber is torsion-free in degrees n and n+1, then the degree-n Hodge polygon of the generic fiber lies on or below the abstract Hodge polygon of the special fiber. We illustrate these comparisons with explicit examples.

Related

  1. Sn-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products
    Mohammadali Aligholi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  2. Generic vanishing for Dolbeault cohomology of mixed Hodge modules on abelian varieties
    Ze Yun
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Exact Generic Exponents of Approximation for the Action of the Integral Special Linear Group on the Torus
    Faustin Adiceam, Régis Aolo
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryDynamical systemsarXiv
  4. Hermitian K-theory for stable ∞-categories III: Grothendieck--Witt groups of rings
    Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
    Annals of MathematicsPeer-reviewedLicence not statedFull text52 citedMathematical physicsOpenAlex
  5. On the Witt liftability of quasi-F-split Calabi--Yau varieties
    Teppei Takamatsu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{yang2026generic,
  title = {{Generic Hodge and special Hodge--Witt polygons}},
  author = {Yuan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05892},
  eprint = {2610.05892},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05892},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generic Hodge and special Hodge--Witt polygons
AU  - Yuan Yang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.05892
UR  - https://arxiv.org/abs/2610.05892
AB  - We show that, in equal characteristic p, the Hodge-Witt polygon can only move down and domino numbers can only increase under specialization in smooth proper families. We also show that the Hodge polygon of the generic fiber of a proper smooth p-adic formal scheme over 𝒪_C lies on or above the Hodge-Witt polygon of its special fiber, where C is a complete algebraically closed extension of ℚ_p. We further show that, in this mixed-characteristic setting, if the crystalline cohomology of the special fiber is torsion-free in degrees n and n+1, then the degree-n Hodge polygon of the generic fiber lies on or below the abstract Hodge polygon of the special fiber. We illustrate these comparisons with explicit examples.
ER  -