The Euler system of Beilinson-Flach elements and Gross-Stark units.

The Euler system of Beilinson-Flach elements and Gross-Stark units.

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Oscar Rivero Salgado, Universitat Politecnica de Catalunya
Fine Hall 214

Kings, Loeffler and Zerbes constructed an Euler system of Beilinson-Flach elements attached to two Hida families and prove an explicit reciprocity law in that case. In this talk, we focus on the self-dual case, where an exceptional zero phenomenon emerges and the connection with the Hida-Rankin p-adic L-function is now via the derived Belinson-Flach elements. At the same time, we see how the weight one specialization of this derived class encodes arithmetic information concerning the group of units of the associated number fields.