View source for Faltings's product theorem

In [[Arithmetic geometry|arithmetic geometry]], the '''Faltings's product theorem''' gives sufficient conditions for a [[Algebraic variety|subvariety]] of a product of [[Projective space|projective space]]s to be a product of varieties in the projective spaces. It was introduced by {{harvs|txt|last=Faltings|year=1991|}} in his proof of Lang's conjecture that subvarieties of an [[Abelian variety|abelian variety]] containing no translates of non-trivial abelian subvarieties have only finitely many rational points.
{{harvtxt|Evertse|1995}} and {{harvtxt|Ferretti|1996}} gave explicit versions of the Faltings's product theorem.

==References==
*{{Citation | last1=Evertse | first1=Jan-Hendrik | title=An explicit version of Faltings' product theorem and an improvement of Roth's lemma | url=http://matwbn.icm.edu.pl/ksiazki/aa/aa73/aa7332.pdf |mr=1364461 | year=1995 | journal=[[Acta Arithmetica]] | issn=0065-1036 | volume=73 | issue=3 | pages=215–248| doi=10.4064/aa-73-3-215-248 }}
*{{Citation | last1=Faltings | first1=Gerd | title=Diophantine approximation on abelian varieties | doi=10.2307/2944319 |mr=1109353 | year=1991 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=133 | issue=3 | pages=549–576| jstor=2944319 }}
*{{Citation | last1=Ferretti | first1=Roberto | title=An effective version of Faltings' product theorem | doi=10.1515/form.1996.8.401 |mr=1393322 | year=1996 | journal=Forum Mathematicum | issn=0933-7741 | volume=8 | issue=4 | pages=401–427}}

[[Category:Diophantine approximation]]
[[Category:Theorems in number theory]]



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