Mordell's theorem, which says that the group of rational points on an elliptic curve is finitely generated... Rational Points on Elliptic Curves - Page viii by Joseph H. Silverman, John T. Tate - 1994 - 281 pages Limited preview - About this book
...the Jacobians of modular curves. Chapter IV. Heights In 1922, Mordell proved a conjecture of Poincare that the group of rational points on an elliptic curve is finitely generated. The reader can profitably look at the exposition in his book [Mo]. In 1929-1930, Weil extended this...