Adelic points of elliptic curves

For an elliptic curve defined E over a number field K,
the group of points of E defined over the adele ring of K is a topological group
that may be analyzed in terms of the Galois representation associated to the
torsion points of E.
We give an explicit description of this topological group, and show that for
`almost all' E/K, it is isomorphic to a universal group U_n depending only on
the degree n of K over Q. This is joint work with Athanasios Angelakis.