The Birch--Swinnerton-Dyer conjecture: beyond dimension 1

Lead Research Organisation: University College London
Department Name: Mathematics

Abstract

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Publications

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Loeffler, D (2021) On the Bloch--Kato conjecture for GSp(4) x GL(2)

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Loeffler, D (2021) Spherical varieties and p-adic families of cohomology classes

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Loeffler, D (2021) On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces

 
Description Together with my collaborator David Loeffler, we have proved many new cases of the Birch--Swinnerton-Dyer conjecture for abelian surfaces, making progress on one of the central open problems in mathematics.
Exploitation Route The results of this work are expected to stimulate much new research in number theory and geometry.
Sectors Other