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 A be the Neron model of A over the ring of integers O_k of k. Completing A along its zero section defines a formal group A-circumflex over O_k. We prove that any formal subgroup of the generic fiber of A-circumflex whose closure in A-circumflex 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].
展开▼
