Faltings' product theorem

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.

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, doi:10.4064/aa-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, JSTOR 2944319, 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, S2CID 201091768