Formal subgroups of abelian varieties

In this paper, we generalize the result of [12] in the following sense. Let A be an abelian variety over a number field k, let ? be the Néron model of A over the ring of integers O _k of k. Completing ? along its zero section defines a formal group over O _k . We prove that any formal subgroup of the generic fiber of whose closure in is smooth over an open subset of Spec O _k arises in fact from an abelian subvariety of A. The proof is of a transcendental nature and uses the Arakelovian formalism introduced by Bost [3]. Oblatum 2-V-2000 & 28-XI-2000?Published online: 5 March 2001