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# Faltings product theorem

In arithmetic geometry, the 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 the Falting product theorem.

References

Evertse, Jan-Hendrik (1995), "An explicit version of Faltings' product theorem and an improvement of Roth's lemma" (PDF), Acta Arithmetica 73 (3): 215–248, ISSN 0065-1036, MR 1364461

Faltings, Gerd (1991), "Diophantine approximation on abelian varieties", Annals of Mathematics. Second Series 133 (3): 549–576, doi:10.2307/2944319, ISSN 0003-486X, MR 1109353

Ferretti, Roberto (1996), "An effective version of Faltings' product theorem", Forum Mathematicum 8 (4): 401–427, doi:10.1515/form.1996.8.401, ISSN 0933-7741, MR 1393322

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