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Annihilating tate-shafarevic groups

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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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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