Quaternionic Darmon points and arithmetic applications

In 2001 H. Darmon propossed a systematic construction of local
points on rational elliptic curves using p-adic integration combined
with the theory of modular symbols. Conjecturally, these points should
actually be defined over abelian extensions of real quadratic fields and
their behaviour in the Mordell-Weil group is governed by L-functions, as
much as Heegner points in the case of real imaginary fields. The aim of
the talk is to present a Darmon-style construction in the context of
Shimura curves. I will also give some arithmetic applications of this
theory to the Birch and Swinnerton-Dyer conjecture for rational elliptic
curves over real quadratic fields.