Description
Abstract: During the nineties Kato obtained deep results on the Birch and Swinnerton-Dyer conjecture in rank 0 for twists of elliptic curves over Q by Dirichlet characters. More recently, Bertolini-Darmon-Rotger and Darmon-Rotger developed analogous methods to treat twists by certain Artin representations of dimension 2 and 4. The aim of this talk is to explain the main ideas of joint ongoing work with Molina and Rotger which aims to generalize the methods used by Kato, Bertolini-Darmon-Rotger and Darmon-Rotger to totally real number fields, by exploiting the techniques of Andreatta and Iovita.
