Faltings's theorem

Faltings's theorem

Gerd Faltings
Field	Arithmetic geometry
Conjectured by	Louis Mordell
Conjectured in	1922
First proof by	Gerd Faltings
First proof in	1983
Generalizations	Bombieri–Lang conjecture Mordell–Lang conjecture
Consequences	Siegel's theorem on integral points

Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field ${\displaystyle \mathbb {Q} }$ of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell,^[1] and known as the Mordell conjecture until its 1983 proof by Gerd Faltings.^[2] The conjecture was later generalized by replacing ${\displaystyle \mathbb {Q} }$ by any number field.