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

Abstract

Let E E be an elliptic curve over a number field F F , and let F ∞ F_\infty be a Galois extension of F F whose Galois group G G is a p 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 E over F ∞ F_\infty , and the global root numbers attached to the twists of the complex L L -function of E E by Artin representations of G G .