Faltings' product theorem

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In arithmetic geometry, Faltings' product theorem gives sufficient conditions for a subvariety of a product of projective spaces to be a product of varieties in the projective spaces. It was introduced by Faltings (1991) in his proof of Lang's conjecture that subvarieties of an abelian variety containing no translates of non-trivial abelian subvarieties have only finitely many rational points.

(Evertse 1995) and (Ferretti 1996) gave explicit versions of Faltings' product theorem.