On a generalization of Perrin-Riou's conjecture on Kato's zeta elements

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• Takamichi Sano (Osaka City University and King's College London)
• Tuesday 11 February 2020, 14:30-15:30
• MR13.

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In 1993, Perrin-Riou proposed a conjecture, which relates Kato’s zeta elements for elliptic curves with Heegner points. She showed that her conjecture implies the Mazur-Tate-Teitelbaum conjecture in the rank one case, by using a formula concerning p-adic heights, which was independently obtained by Rubin. One can show that the Iwasawa main conjecture combined with Perrin-Riou’s conjecture implies the (p-part of the) Birch-Swinnerton-Dyer formula in the rank one case, although this is not mentioned in Perrin-Riou’s work. In this talk, I will propose a generalization of Perrin-Riou’s conjecture by introducing a “Bockstein regulator” and generalize the results above to elliptic curves of arbitrary rank. This is joint work with D. Burns and M. Kurihara.

This talk is part of the Number Theory Seminar series.

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