## STNB2018 (32nd edition)

### Big Heegner points and some cases of the Bloch-Kato conjecture

#### Presenters

Francesc Fité Naya

#### Abstract

In this talk, we will explain Castellà's result on some rank 0 cases of the Bloch-Kato conjecture for twists of newforms by certain anticyclotomic Hecke characters. The strategy of the proof combines: 1) the existence of a big $p$-adic regulator map that connects the $p$-adic $L$-function introduced in the second talk with the Big Heegner point defined in the third talk, and 2) Fouquet's generalization of the Kolyvagin method seen in the first talk.