Mordell–Weil theorem

《Diophantine Geometry: An Introduction》 · Introduction；印刷第 257 页，Part C，Theorem C.0.1

Mordell-Weil Theorem. The group of rational points on an abelian variety is finitely generated. […] Let $A$ be an abelian variety defined over a number field $k$. Then the group $A(k)$ of $k$-rational points of $A$ is finitely generated.