NAG

Abstract

We describe how main conjectures in non-commutative Iwasawa theory lead naturally to the (conjectural) construction of a family of explicit annihilators of the Bloch-Kato-Tate-Shafarevic Groups that are attached to a wide class of p-adic representations over non-abelian extensions of number fields. Concrete examples to be discussed include a natural non-abelian analogue of Stickelberger's Theorem (which is proved) and of the refinement of the Birch and Swinnerton-Dyer Conjecture due to Mazur and Tate. Parts of this talk represent joint work with James Barrett and Henri Johnston.