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

Abstract

We formulate analogues of the Birch and Swinnerton-Dyer conjecture for the p-adic L-functions of Bertolini, Darmon, and 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.