The geometric classification of smooth projective curves admitting infinitely many points of degree d≤5 extends from number fields to function fields of characteristic 0 via specialization.
Gao, A complete proof of the geometric bombieri-lang conjecture for ramified covers of abelian varieties, arXiv:2511.17010 https://arxiv.org/pdf/2511.17010
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Points of low degree on curves over function fields
The geometric classification of smooth projective curves admitting infinitely many points of degree d≤5 extends from number fields to function fields of characteristic 0 via specialization.