Equidistribution of small points over finitely generated fields

@misc{guo2026equidistribution,
  title = {{Equidistribution of small points over finitely generated fields}},
  author = {Ruoyi Guo and Lai Shang and Chengyuan Yang and Xinyi Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07716},
  eprint = {2609.07716},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07716},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Equidistribution of small points over finitely generated fields
AU  - Ruoyi Guo
AU  - Lai Shang
AU  - Chengyuan Yang
AU  - Xinyi Yuan
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07716
UR  - https://arxiv.org/abs/2609.07716
AB  - We study the equidistribution of small points over finitely generated fields, in connection with a conjecture of Yuan--Zhang. We first give a counterexample showing that numerical smallness, defined using Moriwaki heights for all polarizations, does not imply equidistribution at every valuation. We then prove that numerically small points do equidistribute at every fully transcendental valuation. In particular, when F is the function field of a curve B/ℚ, these valuations correspond to points of types 2, 3, and 4 in the Berkovich analytification of B_ℚ_p.
ER  -