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.
Koll\' a r, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete
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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.