Root numbers, Selmer groups, and non-commutative Iwasawa theory

Abstract

Let E be an elliptic curve over a number field F, and let F_∞ be a Galois extension of F whose Galois group G is a p-adic Lie group. The aim of the present paper is to provide some evidence that, in accordance with the main conjectures of Iwasawa theory, there is a close connection between the action of the Selmer group of E over F_∞, and the global root numbers attached to the twists of the complex L-function of E by Artin representations of G.