University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > From the order of vanishing of $L$-function of elliptic curves to the universal main conjecture for eigencuspforms and back

From the order of vanishing of $L$-function of elliptic curves to the universal main conjecture for eigencuspforms and back

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

In the early 1960s, B. Birch and P. Swinnerton-Dyer formulated a bold conjecture stating that the order of vanishing of the $L$-function of a rational elliptic curve at $s=1$ is equal to the rank of its group of rational points. In this talk, we explain how to prove that one of these number is equal to zero if and only if the other is and why the proof requires (at present, at least) a very long detour through Iwasawa theory of universal deformation spaces. This is joint work with X. Wan.

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

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