Mordell–Weil theorem
The group of K-rational points of an abelian variety is a finitely-generated abelian group / From Wikipedia, the free encyclopedia
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In mathematics, the Mordell–Weil theorem states that for an abelian variety over a number field , the group of K-rational points of is a finitely-generated abelian group, called the Mordell–Weil group. The case with an elliptic curve and the field of rational numbers is Mordell's theorem, answering a question apparently posed by Henri Poincaré around 1901; it was proved by Louis Mordell in 1922. It is a foundational theorem of Diophantine geometry and the arithmetic of abelian varieties.
Quick Facts Field, Conjectured by ...
Field | Number theory |
---|---|
Conjectured by | Henri Poincaré |
Conjectured in | 1901 |
First proof by | André Weil |
First proof in | 1929 |
Generalizations | Faltings's theorem Bombieri–Lang conjecture Mordell–Lang conjecture |
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