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PreprintCC BY 4.0arXiv

Uniform Mordell--Lang conjecture for semiabelian varieties

  • Zhaobo Han
  • Wenbin Luo
  • Jiawei Yu
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Abstract

We prove the uniform Mordell--Lang conjecture for semiabelian varieties, that is, for a subvariety X of a semiabelian variety, its intersection with a finite-rank subgroup of rational points, can be covered by at most c cosets contained in X, where c depends only on the dimension of the semiabelian variety, the degree of X, and the rank of the subgroup. Our proof is new even in the abelian case previously proven by Gao--Ge--Kühne.

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Cite

BibTeXRIS
BibTeX
@misc{han2026uniform,
  title = {{Uniform Mordell--Lang conjecture for semiabelian varieties}},
  author = {Zhaobo Han and Wenbin Luo and Jiawei Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.17233},
  eprint = {2609.17233},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17233},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Uniform Mordell--Lang conjecture for semiabelian varieties
AU  - Zhaobo Han
AU  - Wenbin Luo
AU  - Jiawei Yu
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.17233
UR  - https://arxiv.org/abs/2609.17233
AB  - We prove the uniform Mordell--Lang conjecture for semiabelian varieties, that is, for a subvariety X of a semiabelian variety, its intersection with a finite-rank subgroup of rational points, can be covered by at most c cosets contained in X, where c depends only on the dimension of the semiabelian variety, the degree of X, and the rank of the subgroup. Our proof is new even in the abelian case previously proven by Gao--Ge--Kühne.
ER  -