STNB2017, (31st edition)
The Mazur-Tate-Teitelbaum conjecture in the rank one setting.
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Abstract
We shall explain Rodolfo Venerucci's results on the Mazur-Tate-Teitelbaum exceptional zero conjecture for the $p$-adic $L$-function of an elliptic curve $E/\mathbb{Q}$ of Mordell-Weil rank 1. The key point of the argument is the interplay between the Euler systems of Heegner points and Beilinson-Kato elements. A fundamental tool employed in the proof is the theory of $p$-adic variation of modular forms, special values of $L$-functions and logarithms of cycle classes. Reference: [Ven16]
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