Aleksander Horawa

The equivariant BSD conjecture via p-adic L-functions

(Joint work with Luca Dall’ava.) We will explain a p-adic method to investigate the BSD conjecture: we will construct a p-adic point on a rational elliptic curve, which is conjecturally defined over a specific number field. In special cases, this recovers the famous Heegner point construction. Our method applies to cases where the relevant part of the Mordell—Weil group is rank one and is related to balanced triple product L-functions. This complements previous work of Darmon—Lauder—Rotger about rank two cases and unbalanced p-adic L-functions.