On anticyclotomic variants of the p-adic Birch and Swinnerton-Dyer conjecture

2019/10/19 by Adebisi Agboola, Agboola, Adebisi, Francesc Castella +1 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1910.08680

23 pages

arxiv created 2019/10/19 · arxiv updated 2019/10/22

Abstract

We formulate analogues of the Birch and Swinnerton-Dyer conjecture for the p-adic L-functions of Bertolini-Darmon-Prasanna attached to elliptic curves E/Q at primes p of good ordinary reduction. Using Iwasawa theory, we then prove under mild hypotheses one of the inequalities predicted by the rank part of our conjectures, as well as the predicted leading coefficient formula up to a p-adic unit. Our conjectures are very closely related to conjectures of Birch and Swinnerton-Dyer type formulated by Bertolini-Darmon in 1996 for certain Heegner distributions, and as application of our results we also obtain the proof of an inequality in the rank part of their conjectures.

Cited by

• On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters

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