Title: Adelic point groups of elliptic curves,
Abstract: We show that for an elliptic curve E defined over a number field K, the group
E(A) of points of E over the adele ring A of K is a topological group that can
be analyzed in terms of the Galois representation associated to the torsion
points of E. An explicit description of E(A) is given, and we prove that for K
of degree n, almost all elliptic curves over K have an adelic point group
topologically isomorphic to a universal group depending on n. We also show that
there exist infinitely many elliptic curves over K having a different adelic
point group.