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.
History
The analytic subgroup theorem was proved in 2007 by Alan Baker and Gisbert Wüstholz.
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.
See also
References
- Baker, Alan; Wüstholz, Gisbert (2007). Logarithmic Forms and Diophantine Geometry. New Mathematical Monographs. Vol. 9. Cambridge: Cambridge University Press. ISBN 978-0-521-88268-2. MR 2382891.