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.

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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