Refined conjectures of Birch and Swinnerton-Dyer type

Abstract: In analogy to Stickelberger's Theorem and refining the Birch—Swinnerton-Dyer Conjecture, Mazur—Tate conjecture an order of vanishing and main conjecture for a certain group ring element. This element is defined in terms of modular symbols and relates to the twisted Hasse—Weil $L$-series of elliptic curves. In this talk I will explain the conjectures of Mazur—Tate and report on work in progress, joint with Dominik Bullach, in which we prove new results towards these conjectures.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html