慶應義塾大学 理工学部 数理科学科

代数セミナー

タイトル p-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou
開催日時 2019年1月9日 16:30-17:30
主催者
講演者 Kazim Buyukboduk 氏 (UC Dublin)
場所 矢上キャンパス 14棟631A/B室
内容 I will report joint work in progress with R. Pollack and S. Sasaki, where we prove a p-adic Gross-Zagier formula for critical slope p-adic L-functions. Besides the strategy for our proof, I will illustrate a number of applications. The first is the proof of a conjecture of Perrin-Riou, which predicts an explicit construction of the generator of the Mordell-Weil group in terms of p-adic L-values when the analytic rank is one. The second is towards a Birch and Swinnerton-Dyer formula when the analytic rank is one, yielding an improvement of the recent results of Jetchev-Skinner-Wan in this context (and simplifying their proof).
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