Local-global divisibility of rational points in some commutative algebraic groups
Roberto Dvornicich, Umberto Zannier (2001)
Bulletin de la Société Mathématique de France
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Let be a commutative algebraic group defined over a number field . We consider the following question:A complete answer for the case of the multiplicative group is classical. We study other instances and in particular obtain an affirmative answer when is a prime and is either an elliptic curve or a torus of small dimension with respect to . Without restriction on the dimension of a torus, we produce an example showing that the answer can be negative even when is a prime. ...