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On the finite transcendence of Frobenius traces for abelian varieties over ℚ

  • Yuto Tsuruta
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Abstract

The first purpose of this paper is to give the fnite transcendence of Frobenius traces for elliptic curves over ℚ without the assumption of complex multiplication (CM). This result generalizes the previous work by Luca and Zudilin, who obtained similar transcendence results specifically for the CM case. The second purpose is to give the finite transcendence of Frobenius traces for several principally polarized abelian varieties over ℚ, by using Luca--Zudilin's method.

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Cite

BibTeXRIS
BibTeX
@misc{tsuruta2026finite,
  title = {{On the finite transcendence of Frobenius traces for abelian varieties over $\mathbbQ$}},
  author = {Yuto Tsuruta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.17674},
  eprint = {2605.17674},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.17674},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - On the finite transcendence of Frobenius traces for abelian varieties over ℚ
AU  - Yuto Tsuruta
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2605.17674
UR  - https://arxiv.org/abs/2605.17674
AB  - The first purpose of this paper is to give the fnite transcendence of Frobenius traces for elliptic curves over ℚ without the assumption of complex multiplication (CM). This result generalizes the previous work by Luca and Zudilin, who obtained similar transcendence results specifically for the CM case. The second purpose is to give the finite transcendence of Frobenius traces for several principally polarized abelian varieties over ℚ, by using Luca--Zudilin's method.
ER  -