On the reductions of non-torsion points
(Un exposé de Jing Yu au séminaire de théorie des
nombres de Chevaleret le 13 mai 2002)
Résumé :
Given a commutative algebraic group $G$ defined
over a global field, and a non-torsion rational
point $P$ on it, we are interested in the orders
of the reduction of that point modulo various
primes. In particular, we ask whether the
occurred orders will cover almost all positive
integers. Replacing algebraic group by Drinfeld
modules, analogous questions can also be asked.
The connection of these problems with linear
forms in logarithms will be explained.