Fedor Pakovich

Algebraic functions with infinitely many values in a number field

We provide several characterizations of algebraic curves X : F ( x , y ) = 0 defined over ℚ ¯ that satisfy the following property: there exist a number field k and an infinite set S ⊂ k such that, for every y ∈ S , the roots of the polynomial F ( x , y ) belong to k .