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PreprintarXiv licencearXiv

Frey-Mazur theorem for semistable elliptic curves over function fields

  • Fateme Sajadi
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Abstract

Let k be a field, let B/k be a smooth projective geometrically integral curve, and put K=k(B). We prove a Frey--Mazur type theorem for nonisotrivial semistable elliptic curves over K. More precisely, after fixing the genus of B and the characteristic of k, a sufficiently large prime-to-characteristic torsion representation determines the K-isogeny class.

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Cite

BibTeXRIS
BibTeX
@misc{sajadi2026freymazur,
  title = {{Frey-Mazur theorem for semistable elliptic curves over function fields}},
  author = {Fateme Sajadi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21529},
  eprint = {2610.21529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21529},
}
RIS
TY  - UNPB
TI  - Frey-Mazur theorem for semistable elliptic curves over function fields
AU  - Fateme Sajadi
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21529
UR  - https://arxiv.org/abs/2610.21529
AB  - Let k be a field, let B/k be a smooth projective geometrically integral curve, and put K=k(B). We prove a Frey--Mazur type theorem for nonisotrivial semistable elliptic curves over K. More precisely, after fixing the genus of B and the characteristic of k, a sufficiently large prime-to-characteristic torsion representation determines the K-isogeny class.
ER  -