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.
Raynaud, Around the M ordell conjecture for function fields and a conjecture of S erge L ang , Algebraic geometry ( T okyo/ K yoto, 1982), Lecture Notes in Math., vol
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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.