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Analytic subgroup theorem
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Analytic subgroup theorem : ウィキペディア英語版
Analytic subgroup theorem
In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms in logarithms. Gisbert Wüstholz proved it in the 1980s.
==Statement==
Let ''G'' be a commutative algebraic group defined over a number field ''K'' and let ''B'' be a subgroup of the complex points ''G''(''C'') defined over ''K''. There are points of ''B'' defined over the field of algebraic numbers if and only if there is a non-trivial analytic subgroup ''H'' of ''G'' defined over a number field such that ''H''(''C'') is contained in ''B''.

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