Arman Shamsi Zargar

Generators and splitting fields of certain elliptic K 3 surfaces

Let k ⊂ ℂ be a number field and ℰ be an elliptic curve defined over k ( t ) that is isomorphic to the generic fiber of an elliptic surface π : 𝒮 ℰ → ℙ k 1 . For any extension 𝒦 ⊆ ℂ of k , the set ℰ ( 𝒦 ( t ) ) of 𝒦 ( t ) -rational points of ℰ is known to be a finitely generated a...