Faltings' product theorem

On when a subvariety of a product of projective spaces is a product of varieties

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 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.

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