Mordell’s theorem

From Elliptic Curve Crypto

Louis Joel Mordell proved [1] that the rational points on an elliptic (or hyperelliptic) curve are finitely generated, by using a beautiful, simple method of infinite descent, which several other authors have also worked out and exhibited since, as one of the classic proofs.

André Weil wrote an extensive doctoral dissertation some six years later [2] on the subject in French, generalizing the theorem to arbitrary Abelian varieties and studying it in great depth. Weil's generalization of Mordell’s theorem is often called the “Mordell–Weil theorem.”