Root numbers and Selmer groups of elliptic curves

The theory of root numbers predicts when elliptic curves over number fields have rational points of infinite order. In this talk, we shall discuss results which bring together the root numbers and non-commutative Iwasawa theory. It is joint work with Coates, Fukaya and Kato, and has connections to some recent work of Rohrlich and T. Dokchitser and V. Dokchitser.The theory of root numbers predicts when elliptic curves over number fields have rational points of infinite order. In this talk, we shall discuss results which bring together the root numbers and non-commutative Iwasawa theory. It is joint work with Coates, Fukaya and Kato, and has connections to some recent work of Rohrlich and T. Dokchitser and V. Dokchitser.