Skip to content
DraconiticResearch
Search Sources API
186,123 studies31 sourcesUpdated 25 min ago
PreprintCC BY-NC-SA 4.0arXiv

Mordell--Weil groups of quasi-elliptic surfaces in characteristic 3

  • Toshiyuki Katsura
Open at sourcePDFDOICite

Abstract

In characteristic p =3, we establish a concrete relationship between the torsion rank of the elementary abelian group of global sections of quasi-elliptic surfaces over the projective line P1 and the p-rank of certain hyperelliptic curves, thereby explaining a mysterious relationship between these two invariants previously observed by I. Dolgachev. As an application, we determine the torsion ranks of the Mordell--Weil groups of a class of quasi-elliptic surfaces.

Related

  1. Finite Symplectic Automorphism Groups of K3 Surfaces in Characteristic Seven
    Bin Wang, Zhiwei Zheng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Positive integral points on Mordell-Schinzel surfaces
    Antoine de Saint Germain, Robin Zhang
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv
  3. An elliptic Calabi-Yau threefold of Mordell-Weil rank twelve
    Dominik Burek
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. K3 surfaces with finite automorphism group in positive characteristic
    Alexandros Vlachos
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Foliations on abelian surfaces in positive characteristic
    Fabrizio Andreatta, Eyal Z. Goren
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{katsura2026mordellweil,
  title = {{Mordell--Weil groups of quasi-elliptic surfaces in characteristic 3}},
  author = {Toshiyuki Katsura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23430},
  eprint = {2609.23430},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23430},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Mordell--Weil groups of quasi-elliptic surfaces in characteristic 3
AU  - Toshiyuki Katsura
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23430
UR  - https://arxiv.org/abs/2609.23430
AB  - In characteristic p =3, we establish a concrete relationship between the torsion rank of the elementary abelian group of global sections of quasi-elliptic surfaces over the projective line P^1 and the p-rank of certain hyperelliptic curves, thereby explaining a mysterious relationship between these two invariants previously observed by I. Dolgachev. As an application, we determine the torsion ranks of the Mordell--Weil groups of a class of quasi-elliptic surfaces.
ER  -