The Mordell-Weil theorem states that the set of rational points on an abelian variety over a number field forms a finitely generated abelian group, hence isomorphic to a group of the form $T \oplus \Z^r$, where $T$ is a finite torsion group. The integer $r\ge 0$ is the **Mordell-Weil rank** of the abelian variety.

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- Last edited by John Cremona on 2018-05-24 16:47:17

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- 2018-05-24 16:47:17 by John Cremona (Reviewed)