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Small degree isogenies between conjugate principally polarized superspecial abelian surfaces

  • Eda Kırımlı
  • Lam L. Pham
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Abstract

Let p>3 be a prime number. We prove that every principally polarized superspecial abelian surface over 𝔽p2 with p2-Frobenius [−p] admits a separable polarized isogeny to its Frobenius conjugate with multiplier at most (p3/2)1/5. This generalizes a recent result of Aubry, Oyono, and Vincent (2026, arXiV:2607.14624) who proved that every supersingular elliptic curve defined over 𝔽̅p admits an isogeny to its Frobenius conjugate with degree at most (p/2)1/3.

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Cite

BibTeXRIS
BibTeX
@misc{kırımlı2026small,
  title = {{Small degree isogenies between conjugate principally polarized superspecial abelian surfaces}},
  author = {Eda Kırımlı and Lam L. Pham},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.17330},
  eprint = {2609.17330},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17330},
}
RIS
TY  - UNPB
TI  - Small degree isogenies between conjugate principally polarized superspecial abelian surfaces
AU  - Eda Kırımlı
AU  - Lam L. Pham
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.17330
UR  - https://arxiv.org/abs/2609.17330
AB  - Let p>3 be a prime number. We prove that every principally polarized superspecial abelian surface over 𝔽_p^2 with p^2-Frobenius [−p] admits a separable polarized isogeny to its Frobenius conjugate with multiplier at most (p^3/2)^1/5. This generalizes a recent result of Aubry, Oyono, and Vincent (2026, arXiV:2607.14624) who proved that every supersingular elliptic curve defined over 𝔽̅_p admits an isogeny to its Frobenius conjugate with degree at most (p/2)^1/3.
ER  -