Derived p-adic heights and the leading coefficient of the Bertolini-Darmon-Prasanna p-adic L-function — Francesc Castella (UC Santa Barbara)

Let E be a rational elliptic curve, p>2 a prime of good reduction for E, and K an imaginary quadratic field such that every prime factor of Np splits in K. In this talk, I will formulate a p-adic analogue of the BSD conjecture for the p-adic L-function of Bertolini-Darmon-Prasanna attached to E/K. Then I will explain what we can prove in the direction of our conjectures building on anticyclotomic Iwasawa theory and Howard's construction of derived p-adic heights.