Matteo Tamiozzo (Université Sorbonne Paris Nord): Towards semi-global plectic conjectures

Known results on the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank at most one over totally real fields rely on CM points on Shimura curves. After recalling this, I will illustrate how an attempt to go beyond rank one leads to the plectic conjectures of Nekovář-Scholl for higher-dimensional quaternionic Shimura varieties. Finally, I will present joint work in progress with Tony Feng and Mingjia Zhang aimed at proving a “semi-global” version of these conjectures.

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